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	<title>Freiman&#039;s theorem - Revision history</title>
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	<updated>2026-04-22T13:32:06Z</updated>
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		<title>en&gt;Rjwilmsi: /* References */Added 1 doi to a journal cite using AWB (10201)</title>
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		<updated>2014-05-22T10:29:40Z</updated>

		<summary type="html">&lt;p&gt;&lt;span class=&quot;autocomment&quot;&gt;References: &lt;/span&gt;Added 1 doi to a journal cite using &lt;a href=&quot;/index.php?title=Testwiki:AWB&amp;amp;action=edit&amp;amp;redlink=1&quot; class=&quot;new&quot; title=&quot;Testwiki:AWB (page does not exist)&quot;&gt;AWB&lt;/a&gt; (10201)&lt;/p&gt;
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				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Revision as of 12:29, 22 May 2014&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l1&quot;&gt;Line 1:&lt;/td&gt;
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&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;{{Advert|date=December 2008}}&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;It is very common to have a dental emergency -- a fractured tooth, an abscess&lt;/ins&gt;, &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;or severe pain when chewing. Over-the-counter pain medication is just masking the problem&lt;/ins&gt;. &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Seeing an emergency dentist is critical to getting the source of the problem diagnosed and corrected as soon as possible.&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;Here are some common dental emergencies:&amp;lt;br&amp;gt;Toothache: The most common dental emergency. This generally means a badly decayed tooth. As the pain affects the tooth&lt;/ins&gt;&#039;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;s nerve, treatment involves gently removing any debris lodged in the cavity being careful not to poke deep as this will cause severe pain if the nerve &lt;/ins&gt;is &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;touched. Next rinse vigorously with warm water. Then soak &lt;/ins&gt;a &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;small piece of cotton in oil &lt;/ins&gt;of &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;cloves and insert it &lt;/ins&gt;in &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;the cavity&lt;/ins&gt;. &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;This will give temporary relief until a dentist can be reached&lt;/ins&gt;.&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;At times &lt;/ins&gt;the &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;pain may have a more obscure location such as decay under an old filling. As this can be only corrected &lt;/ins&gt;by a &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;dentist there are two things you can do to help the pain. Administer a pain pill (aspirin or some other analgesic) internally or dissolve a tablet in a half glass (4 oz) of warm water holding it in the mouth for several minutes before spitting it out. DO NOT PLACE A WHOLE TABLET OR ANY PART OF IT IN THE TOOTH OR AGAINST THE SOFT GUM TISSUE AS IT WILL RESULT IN A NASTY BURN&lt;/ins&gt;.&amp;lt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;br&amp;gt;&amp;lt;br&lt;/ins&gt;&amp;gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Swollen Jaw&lt;/ins&gt;: &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;This may be caused by several conditions the most probable being an abscessed tooth. In any case the treatment should be to reduce pain and swelling&lt;/ins&gt;. &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;An ice pack held on the outside of the jaw, (ten minutes on and ten minutes off) will take care of both&lt;/ins&gt;. &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;If this does not control the pain, an analgesic tablet can be given every four hours&lt;/ins&gt;.&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;Other Oral Injuries: Broken teeth&lt;/ins&gt;, &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;cut lips, bitten tongue or lips if severe means &lt;/ins&gt;a &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;trip &lt;/ins&gt;to &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;a dentist as soon as possible. In the mean time rinse &lt;/ins&gt;the &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;mouth with warm water and place cold compression the face opposite the injury. If there &lt;/ins&gt;is &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;a lot of bleeding&lt;/ins&gt;, &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;apply direct pressure to the bleeding area. If bleeding does not stop get patient to the emergency room of a hospital as stitches may be necessary.&lt;/ins&gt;&amp;lt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;br&lt;/ins&gt;&amp;gt;&amp;lt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;br&lt;/ins&gt;&amp;gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Prolonged Bleeding Following Extraction: Place a gauze pad or better still a moistened tea bag over the socket and have &lt;/ins&gt;the &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;patient bite down gently on it for 30 to 45 minutes. The tannic acid &lt;/ins&gt;in the &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;tea seeps into the tissues and often helps stop the bleeding&lt;/ins&gt;. &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;If bleeding continues after two hours, call the dentist or take patient &lt;/ins&gt;to the &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;emergency room of the nearest hospital.&lt;/ins&gt;&amp;lt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;br&lt;/ins&gt;&amp;gt;&amp;lt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;br&lt;/ins&gt;&amp;gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Broken Jaw: If you suspect the patient&#039;s jaw is broken, bring the upper and lower teeth together&lt;/ins&gt;. &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Put a necktie, handkerchief or towel under the chin, tying it over the head to immobilize &lt;/ins&gt;the &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;jaw until you &lt;/ins&gt;can &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;get the patient to a dentist or &lt;/ins&gt;the &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;emergency room of a hospital&lt;/ins&gt;.&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;Painful Erupting Tooth: In young children teething pain can come from &lt;/ins&gt;a &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;loose baby tooth or from an erupting permanent tooth&lt;/ins&gt;. &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Some relief can &lt;/ins&gt;be &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;given by crushing a little ice and wrapping it in gauze or a clean piece of cloth &lt;/ins&gt;and &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;putting it directly &lt;/ins&gt;on the &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;tooth or gum tissue where it hurts&lt;/ins&gt;. &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;The numbing effect of the cold, along with an appropriate dose of aspirin, usually provides temporary relief&lt;/ins&gt;.&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;In young adults&lt;/ins&gt;, &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;an erupting 3rd molar (Wisdom tooth&lt;/ins&gt;)&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;, especially if it &lt;/ins&gt;is &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;impacted, can cause &lt;/ins&gt;the &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;jaw to swell &lt;/ins&gt;and &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;be quite painful&lt;/ins&gt;. &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Often the gum around &lt;/ins&gt;the &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;tooth will show signs of infection. Temporary relief can be had by giving aspirin or some other painkiller and by dissolving an aspirin in half a glass of warm water &lt;/ins&gt;and &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;holding this solution in the mouth over the sore gum. AGAIN DO NOT PLACE A TABLET DIRECTLY OVER THE GUM OR CHEEK OR USE THE ASPIRIN SOLUTION ANY STRONGER THAN RECOMMENDED TO PREVENT BURNING THE TISSUE&lt;/ins&gt;. &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;The swelling of the jaw can be reduced by using an ice pack on the outside of &lt;/ins&gt;the &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;face at intervals of ten minutes on &lt;/ins&gt;and &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;ten minutes off&lt;/ins&gt;.&amp;lt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;br&lt;/ins&gt;&amp;gt;&amp;lt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;br&lt;/ins&gt;&amp;gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;If you loved this article and you wish to receive more info about &lt;/ins&gt;[http://www.&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;youtube&lt;/ins&gt;.com&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;/watch?v=90z1mmiwNS8 dentist DC&lt;/ins&gt;] &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;assure visit &lt;/ins&gt;the &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;web&lt;/ins&gt;-&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;page&lt;/ins&gt;.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&#039;&#039;&#039;Ntru Cryptosystems&lt;/del&gt;, &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Inc&lt;/del&gt;.&#039;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&#039;&#039; &lt;/del&gt;is a &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;provider &lt;/del&gt;of &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;embedded security solutions.  It was founded &lt;/del&gt;in &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;1996 by [[Joseph H&lt;/del&gt;. &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Silverman]], [[Jeffrey Hoffstein]], [[Jill Pipher]] and [[Daniel Lieman]], four [[mathematicians]] at [[Brown University]]&lt;/del&gt;. &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt; In 2009, &lt;/del&gt;the &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;company was acquired &lt;/del&gt;by &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Security Innovation -- &lt;/del&gt;a &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;software security company&lt;/del&gt;.&amp;lt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;ref&lt;/del&gt;&amp;gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[http&lt;/del&gt;:&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;//www&lt;/del&gt;.&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;securityinnovation&lt;/del&gt;.&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;com/company/releases/si-ntru&lt;/del&gt;.&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;shtml  Security Innovation acquires NTRU Cryptosystems&lt;/del&gt;, &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt; &lt;/del&gt;a &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;leading security solutions provider &lt;/del&gt;to the &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;embedded security market]&amp;lt;/ref&amp;gt;&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;The name Ntru &lt;/del&gt;is &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;short for N-th degree &#039;&#039;tru&#039;&#039;ncated polynomial ring&lt;/del&gt;, &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;or in mathematical notation &lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;:&lt;/del&gt;&amp;lt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;math&lt;/del&gt;&amp;gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;R[x]/(x^N-1)&lt;/del&gt;&amp;lt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;/math&lt;/del&gt;&amp;gt;  &lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;which is &lt;/del&gt;the &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;underlying [[ring (mathematics)|ring]] &lt;/del&gt;in &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;which &lt;/del&gt;the &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;cryptosystem works&lt;/del&gt;. &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;The base ring &#039;&#039;R&#039;&#039; is taken &lt;/del&gt;to &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;be &lt;/del&gt;the &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[[finite field]] &lt;/del&gt;&amp;lt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;math&lt;/del&gt;&amp;gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;\mathbb{Z}/p\mathbb{Z}&lt;/del&gt;&amp;lt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;/math&lt;/del&gt;&amp;gt;. &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt; A detailed description of &lt;/del&gt;the &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;encryption &lt;/del&gt;can &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;be found in &lt;/del&gt;the &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[[NTRUEncrypt]] page&lt;/del&gt;.&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Ntru Cryptosystems has developed and markets &lt;/del&gt;a &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[[Public key cryptography|Public-key cryptosystem]]&lt;/del&gt;. &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt; Ntru appears to &lt;/del&gt;be &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;much faster than its major competitors (namely [[RSA (algorithm)|RSA]]), &lt;/del&gt;and &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;consequently has focused &lt;/del&gt;on the &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;embedded markets (e&lt;/del&gt;.&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;g&lt;/del&gt;., &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;cell Phones and [[RFID]] chips&lt;/del&gt;) &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;where processing power &lt;/del&gt;is &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;scarcer.&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;As is often &lt;/del&gt;the &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;case with cryptographic algorithms, slight modifications allow both [[encryption]] &lt;/del&gt;and &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[[digital signature]]&lt;/del&gt;. &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt; In &lt;/del&gt;the &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Ntru Cryptosystem, these are called [[NTRUEncrypt]] &lt;/del&gt;and &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[[NTRUSign]] respectively&lt;/del&gt;. &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt; Alternative definitions for &lt;/del&gt;the &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;acronym &quot;NTRU&quot; are &quot;Number Theorists aRe Us&quot; &lt;/del&gt;and &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&quot;Number Theory Research Unit&quot;&lt;/del&gt;.&amp;lt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;ref&lt;/del&gt;&amp;gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;{{cite web | url=http://www.brown.edu/Administration/George_Street_Journal/vol25/25GSJ01e.html | title = Three Brown mathematicians build encryption system | author = Janet Kerlin | date = 2007-03-23 | language = English}}&lt;/del&gt;&amp;lt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;/ref&lt;/del&gt;&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;==References==&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;{{Reflist}}&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;==External links==&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;* &lt;/del&gt;[http://www.&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;ntru&lt;/del&gt;.com &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Home page&lt;/del&gt;] &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&amp;amp;mdash; includes information about &lt;/del&gt;the &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;algorithms, and gives up&lt;/del&gt;-&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;to-date information about [[peer review]]s that they have received&lt;/del&gt;.&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[[Category:Cryptography companies]]&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[[Category:Radio-frequency identification]]&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>en&gt;Rjwilmsi</name></author>
	</entry>
	<entry>
		<id>https://en.formulasearchengine.com/index.php?title=Freiman%27s_theorem&amp;diff=10269&amp;oldid=prev</id>
		<title>en&gt;Francois-Pier: + math</title>
		<link rel="alternate" type="text/html" href="https://en.formulasearchengine.com/index.php?title=Freiman%27s_theorem&amp;diff=10269&amp;oldid=prev"/>
		<updated>2013-09-05T10:21:01Z</updated>

		<summary type="html">&lt;p&gt;+ math&lt;/p&gt;
&lt;a href=&quot;https://en.formulasearchengine.com/index.php?title=Freiman%27s_theorem&amp;amp;diff=10269&amp;amp;oldid=241817&quot;&gt;Show changes&lt;/a&gt;</summary>
		<author><name>en&gt;Francois-Pier</name></author>
	</entry>
	<entry>
		<id>https://en.formulasearchengine.com/index.php?title=Freiman%27s_theorem&amp;diff=241817&amp;oldid=prev</id>
		<title>Deltahedron: /* References */ better</title>
		<link rel="alternate" type="text/html" href="https://en.formulasearchengine.com/index.php?title=Freiman%27s_theorem&amp;diff=241817&amp;oldid=prev"/>
		<updated>2012-06-24T19:32:23Z</updated>

		<summary type="html">&lt;p&gt;&lt;span class=&quot;autocomment&quot;&gt;References: &lt;/span&gt; better&lt;/p&gt;
&lt;p&gt;&lt;b&gt;New page&lt;/b&gt;&lt;/p&gt;&lt;div&gt;== there are lotus. ==&lt;br /&gt;
&lt;br /&gt;
In a lot of colorful lotus land records.&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;ordinary barrel. Also half-human Heights barrel. Half a bucket can be.&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;and this pond. Nearly circular shape. About nearly two meters in diameter, so big pond. Inside the one yuan heavy water. Estimated to be sufficient to store ten barrels of heavy water to one yuan.&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;both ends of [http://www.lamartcorp.com/modules/mod_menu/rakuten_cl_1.php クリスチャンルブタン 靴 メンズ] the pond in the [http://www.lamartcorp.com/modules/mod_menu/rakuten_cl_5.php クリスチャンルブタン バッグ] yuan heavy water. Zhang Lin just two colorful, colorful lotus really look the same as [http://www.lamartcorp.com/modules/mod_menu/rakuten_cl_4.php クリスチャンルブタン セール] described in the reel. Lotus is divided into 288, lotus minimal, there are lotus.&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;&amp;#039;Huh?&amp;#039; Qin [http://www.lamartcorp.com/modules/mod_menu/rakuten_cl_3.php クリスチャンルブタン 靴] Yu suddenly surprised again.&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;&amp;#039;central pond is arranged a little to hide the magic circle.&amp;#039; Qin Yu force to explore space discovered. This pond central in the end what is being used to hide the magic array block.&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;the passage of time, then quickly passed more than three years, more than three years time. [http://www.lamartcorp.com/modules/mod_menu/rakuten_cl_5.php クリスチャンルブタン バッグ] Liu Yuxi talks nine were sitting cross-legged cry in silence, Qin Yu himself sitting cross-legged in the room heard in silence.&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;retreat at the child in the Qin Yu. Suddenly sensed glare to light, when the struggle to open the eyes and yang&lt;br /&gt;
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&lt;br /&gt;
== leading to a lot of other galaxies Chuansong Zhen. ==&lt;br /&gt;
&lt;br /&gt;
Seeking heart.&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;&amp;#039;Yu Huang Majesty broad-minded, will not ......&amp;#039;&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;see Emperor Xian Yu also persuade the Vatican, Qin Yu busy hand nonchalantly said: &amp;#039;Well, I do not have time and クリスチャンルブタン 店舗 you nonsense, leave&amp;#039; Qin Yu finished the whole person speed channeling out, after a great diversion again disappeared.&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;Qin Yu next destination &amp;#039;blue star.&amp;#039;&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;blue star, as Angelica galactic core planet, this planet in Star Chuansong Zhen course very much, traffic developed, leading to a lot of other galaxies Chuansong Zhen.&amp;lt;br&amp;gt;&amp;#039;Friends dark astral ......&amp;#039;&amp;lt;br&amp;gt;Emperor Xian Yu Vatican wants to follow to catch up.&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;&amp;#039;seems only to let クリスチャンルブタン 偽物 Yu Huang personally resolved, I do not know where now arrived.&amp;#039; Bai star in his own to start a summons to Yu Huang, unfortunately there is no communications success.&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;Yu クリスチャンルブタン メンズ 靴 Wong and because he is too far away, only to be summoned クリスチャンルブタン 偽物 within the &amp;#039;maze Communications&amp;#039; success. Vatican last Emperor Xian Yu Lian cents or so ice will matter to Yu Huang Di reporting.&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;Emperor Xian Lian from クリスチャンルブタン通販 the ice to his arraignment&lt;br /&gt;
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&lt;br /&gt;
== palace courtyard alone among the Qin Yu ==&lt;br /&gt;
&lt;br /&gt;
Had lost a war and key central repair, while wind figs, QIN talk about the problem of comprehension aspects. As for the injury itself, Qin Yu, has long been [http://www.lamartcorp.com/modules/mod_menu/rakuten_cl_8.php クリスチャンルブタン 店舗 東京] a popular tears repaired.&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;palace courtyard alone among the Qin [http://www.lamartcorp.com/modules/mod_menu/rakuten_cl_10.php クリスチャンルブタン 値段] Yu, Yu Qin, Qin Feng, Qin Zheng, QIN, wind figs five people sitting around the stone table, at the moment on the stone table stood three Cheats, it had left Qin [http://www.lamartcorp.com/modules/mod_menu/rakuten_cl_4.php クリスチャンルブタン セール] Yu three comprehension Cheats.&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;&amp;#039;Kohane, these three cheats you, you and I have seen the wind uncle, you wind uncle say, this three Cheats comprehension of each of the circles are uppermost comprehension Cheats, you wind uncle are now discarded Over the past practice of law, the use of this method of the above first comprehension. &amp;#039;QIN smile.&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;wind figs also exclaimed: &amp;#039;Kohane is the original Munekado secret pass to [http://www.lamartcorp.com/modules/mod_menu/rakuten_cl_3.php クリスチャンルブタン 東京] practice law, but I also know the secret of Yuan Ying gas only, but obviously not as good as these cheats so deep so proud of mysterious practice of law, it is estimated. Munekado town than we have severe cases of canon. &amp;#039;&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;Qin Yu [http://www.lamartcorp.com/modules/mod_menu/rakuten_cl_0.php クリスチャンルブタン 店舗] is not talking, but with one hand stretched, spiritual goods is five knives and a black rifles floating&lt;br /&gt;
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== &amp;#039;Nothing ==&lt;br /&gt;
&lt;br /&gt;
Other tribe still mulberry family palace. &amp;#039;&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;&amp;#039;Nothing, in the other direction, I have arranged the tribe.&amp;#039;&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;Sang Mo exposed face of evil spirits, while red robe yixian moment, the people turning to red giant octopus, eight Rouzhu startled, of&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;towards the south for a streamer will recover the past, Qin Yu faster than the one who is faster on the trace.&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;......&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;are flying speed towards the south [http://www.lamartcorp.com/modules/mod_menu/rakuten_cl_4.php クリスチャンルブタン 店舗] Qin [http://www.lamartcorp.com/modules/mod_menu/rakuten_cl_12.php クリスチャンルブタンジャパン] Yu suddenly stopped.&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;&amp;#039;someone!&amp;#039;&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;his spiritual knowledge has clearly found dozens of miles away octopus dozen family tribe, although now found only a dozen, but who knows&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;if there are more. Sang Mo bound to have come directly toward their location, Qin Yu had a judge.&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;&amp;#039;That Sang ink know where I am, but also the formation of encirclement.&amp;#039;&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;stopped for a moment in the Qin Yu Qin Yu spiritual knowledge found behind dozens of miles away [http://www.lamartcorp.com/modules/mod_menu/rakuten_cl_4.php クリスチャンルブタン パンプス] to have a huge red giant [http://www.lamartcorp.com/modules/mod_menu/rakuten_cl_2.php クリスチャンルブタン 東京] octopus came the [http://www.lamartcorp.com/modules/mod_menu/rakuten_cl_14.php クリスチャンルブタン 銀座] claws.&lt;br /&gt;
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== &amp;#039; Octagon Chinese ==&lt;br /&gt;
&lt;br /&gt;
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== one of the two ==&lt;br /&gt;
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Patient, the left one laugh loudly: &amp;#039;I variability higher animal body but &amp;#039;double first dragon eagle&amp;#039;, one of [http://www.lamartcorp.com/modules/mod_menu/rakuten_cl_4.php クリスチャンルブタン セール] the two, but the memory of gifted supernatural heritage, you can just hit me a deity to par, strength is also quite good, but with two people on me, you are not [http://www.lamartcorp.com/modules/mod_menu/rakuten_cl_14.php クリスチャンルブタン アウトレット] the opponent. &amp;#039;&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;Qin Yu Ao dry heard saying, silent, suddenly Qin Yu a blind eye.&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;&amp;#039;Fei Fei, black, do not fight, and soon to come.&amp;#039; Qin Yu quietly acoustic road.&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;and Hakuho at the moment is killing Hou Fei, black feather hear acoustic Qin Yu, they strongly believe that Qin Yu, directly aside Hakuho speed fly over toward the Qin Yu, Yu Qin mind a move directly to [http://www.lamartcorp.com/modules/mod_menu/rakuten_cl_12.php クリスチャンルブタン 値段] Hou Fei, black feather duo income the Jiang Lan.&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;&amp;#039;fee fee, black, you first back Jiang Lan, I&amp;#039;ll be right back.&amp;#039; Qin Yu acoustic sounded in [http://www.lamartcorp.com/modules/mod_menu/rakuten_cl_6.php クリスチャンルブタン 中古] Hou Fei, black feather two minds.&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;&amp;#039;brush!&amp;#039;&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;Hakuho silhouette of a sudden the two [http://www.lamartcorp.com/modules/mod_menu/rakuten_cl_0.php ﻿クリスチャンルブタン] Ao dry side, wondering:. &amp;#039;Ao dry, black feather and Hou fees are gone.&amp;#039;&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;two Ao&lt;br /&gt;
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		<author><name>Deltahedron</name></author>
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