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en>Schubi87: Two lines in an array is not supported by MathML (https://phabricator.wikimedia.org/T75169)

2015-01-10T13:24:05Z

Two lines in an array is not supported by MathML (https://phabricator.wikimedia.org/T75169)

← Older revision		Revision as of 15:24, 10 January 2015
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	~~Hi there. My name~~ is ~~Sophia Meagher although it is not the [http://hknews~~.~~classicmall.com.hk/groups/some-simple-tips-for-personal-development-progress/ tarot card readings] title on my birth certification~~. One of ~~the extremely best issues in the world for him~~ is ~~performing ballet and~~ he'~~ll be beginning something [http://mybrandcp.com/xe/board_XmDx25/107997 psychic readings] else along~~ with it. ~~Invoicing~~ is ~~my occupation. I've always cherished residing in Kentucky~~ but ~~now I'm considering other choices~~.<br><br>My blog ~~:: love psychics (~~[http://~~koreanyelp~~.com/~~index.php?document_srl=1798&mid=SchoolNews koreanyelp~~.~~com~~])		Hello, my title is Felicidad but I don't like when people use my complete title. Some time ago he chose to live in Idaho. One of his favorite hobbies is playing crochet but he hasn't produced a dime with it. His working day occupation is a monetary officer but he plans on altering it.<br><br>my blog ... [http://Www.itcomplianceexperts.com/UserProfile/tabid/165/userId/36272/Default.aspx auto warranty]

en>John of Reading: Reverted 1 edit by 182.72.248.90 (talk) to last revision by Schmock. (TW)

2014-03-04T09:36:43Z

Reverted 1 edit by 182.72.248.90 (talk) to last revision by Schmock. (TW)

← Older revision		Revision as of 11:36, 4 March 2014
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	~~In mathematics, a '''Frey curve''' or '''Frey–Hellegouarch''' curve~~ is the [~~[elliptic curve]]~~		Hi there. My name is Sophia Meagher although it is not the [http://hknews.classicmall.com.hk/groups/some-simple-tips-for-personal-development-progress/ tarot card readings] title on my birth certification. One of the extremely best issues in the world for him is performing ballet and he'll be beginning something [http://mybrandcp.com/xe/board_XmDx25/107997 psychic readings] else along with it. Invoicing is my occupation. I've always cherished residing in Kentucky but now I'm considering other choices.<br><br>My blog :: love psychics ([http://koreanyelp.com/index.php?document_srl=1798&mid=SchoolNews koreanyelp.com])
	:~~:<math>y^2 = x(x - a^\ell)(x + b^\ell)\ <~~/~~math>~~
	~~associated with a solution of Fermat's equation~~
	~~:<math>a^\ell + b^\ell = c^\ell~~.~~\ <~~/~~math>~~

	~~==History==~~
	~~{{harvs\|first=Yves\|last=Hellegouarch\|year=1975\|txt}} came up with the idea of associating solutions (a,b,c) of Fermat's equation with a completely different mathematical object: an elliptic curve.~~
	~~If ℓ is an odd prime and ''a'', ''b'', and ''c'' are positive integers such that~~

	~~:<math>a^\ell + b^\ell = c^\ell,\ <~~/~~math>~~

	~~then a corresponding Frey curve is an algebraic curve given by the equation~~

	~~:<math>y^2 = x(x~~ - ~~a^\ell)(x + b^\ell)\ </math>~~

	~~or, equivalently~~

	~~:<math>y^2 = x(x~~ - ~~a^\ell)(x~~ - ~~c^\ell).\ <~~/~~math>~~

	~~This is a nonsingular algebraic curve of genus one defined over '''Q''', and its [[projective completion~~]~~] is an elliptic curve over '''Q'''~~.

	~~{{harvs\|first=Gerhard\|last=Frey\|authorlink=Gerhard Frey\|year=1982}} called attention to~~ the ~~unusual properties of~~ the ~~same curve as Hellegouarch, which became called a Frey curve. This provided a bridge between Fermat~~ and ~~Taniyama by showing that a counterexample to [[Fermat~~'~~s Last Theorem]] would create such a curve that would not~~ be ~~modular. The conjecture attracted considerable interest when {{harvtxt\|Frey\|1986}} suggested that the [[Taniyama–Shimura–Weil conjecture]] implies Fermat's Last Theorem.~~ However, his argument was not complete. In 1985, Jean-Pierre Serre proposed that a Frey curve could not be modular and provided a partial proof of this. This showed that a proof of the semistable case of the Taniyama-Shimura conjecture would imply Fermat's Last Theorem. Serre did not provide a complete proof and what was missing became known as the [[~~epsilon conjecture]] or ε-conjecture. In the summer of 1986, Ribet (1990) proved the epsilon conjecture, thereby proving that the Taniyama–Shimura–Weil conjecture implied Fermat's Last Theorem.~~

	~~==References==~~

	*{{Citation \| last1=Frey \| first1=Gerhard \| title=Links between stable elliptic curves and certain Diophantine equations \| mr=853387 \| year=1986 \| journal=Annales Universitatis Saraviensis. Series Mathematicae \| issn=0933-8268 \| volume=1 \| issue=1 \| pages=iv+40}}
	*{{Citation \| last1=Frey \| first1=Gerhard \| title=Rationale Punkte auf Fermatkurven und getwisteten Modulkurven\| year=1982 \| journal=J.reine u.angew.Math \| volume=331 \| pages=185–191}}
	*{{Citation \| last1=Hellegouarch \| first1=Yves \| title=Rectificatif à l'article de H. Darmon intitulé : "La Conjecture de Shimura-Taniyama-Weil est enfin démontré" \| url=http://~~www~~.~~math.unicaen.fr~~/~~~nitaj~~/~~hellegouarch~~.~~html \| year=2000 \| journal=Gazette des Mathématiciens \| issn=0224-8999 \| volume=83}}~~
	*{{Citation \| last1=Hellegouarch \| first1=Yves \| title=Points d'~~ordre 2p~~<~~sup~~>h<~~/sup~~> ~~sur les courbes elliptiques \| url=~~http://~~matwbn.icm.edu~~.pl/~~tresc~~.php?~~wyd~~=6&~~tom=26 \| mr=0379507 \| year~~=~~1974 \| journal=Polska Akademia Nauk~~. ~~Instytut Matematyczny. Acta Arithmetica \| issn=0065-1036 \| volume=26 \| issue=3 \| pages=253–263}}~~
	*{{Citation \| last1=Hellegouarch \| first1=Yves \| title=Invitation to the mathematics of Fermat-Wiles \| publisher=[[Academic Press]] \| location=Boston, MA \| isbn=978-0-12-339251-0 \| mr=1475927 \| year=2002}}

	~~[[Category:Number theory]~~]

en>David Biddulph: Reverted edits by Limeluis (talk) to last version by 86.136.154.18

2014-02-01T19:00:51Z

Reverted edits by Limeluis (talk) to last version by 86.136.154.18

← Older revision		Revision as of 21:00, 1 February 2014
Line 1:		Line 1:
	~~Claude~~ is ~~her title and she~~ completely ~~digs that name~~. ~~My home~~ is ~~now in Kansas. The preferred pastime for my kids~~ and ~~me is dancing~~ and ~~now I~~'~~m attempting to make cash with it. Managing people~~ is ~~what I do in my day job.~~<br><br>~~Feel free~~ to ~~visit my website;~~ [http://~~sceltic~~.at/~~index~~.~~php?mod~~=~~users&action~~=~~view&id~~=~~51301~~ http://~~sceltic~~.at/~~index~~.php?~~mod~~=~~users~~&~~action~~=~~view&id~~=~~51301~~]		In mathematics, a '''Frey curve''' or '''Frey–Hellegouarch''' curve is the [[elliptic curve]]
			::<math>y^2 = x(x - a^\ell)(x + b^\ell)\ </math>
			associated with a solution of Fermat's equation
			:<math>a^\ell + b^\ell = c^\ell.\ </math>

			==History==
			{{harvs\|first=Yves\|last=Hellegouarch\|year=1975\|txt}} came up with the idea of associating solutions (a,b,c) of Fermat's equation with a completely different mathematical object: an elliptic curve.
			If ℓ is an odd prime and ''a'', ''b'', and ''c'' are positive integers such that

			:<math>a^\ell + b^\ell = c^\ell,\ </math>

			then a corresponding Frey curve is an algebraic curve given by the equation

			:<math>y^2 = x(x - a^\ell)(x + b^\ell)\ </math>

			or, equivalently

			:<math>y^2 = x(x - a^\ell)(x - c^\ell).\ </math>

			This is a nonsingular algebraic curve of genus one defined over '''Q''', and its [[projective completion]] is an elliptic curve over '''Q'''.

			{{harvs\|first=Gerhard\|last=Frey\|authorlink=Gerhard Frey\|year=1982}} called attention to the unusual properties of the same curve as Hellegouarch, which became called a Frey curve. This provided a bridge between Fermat and Taniyama by showing that a counterexample to [[Fermat's Last Theorem]] would create such a curve that would not be modular. The conjecture attracted considerable interest when {{harvtxt\|Frey\|1986}} suggested that the [[Taniyama–Shimura–Weil conjecture]] implies Fermat's Last Theorem. However, his argument was not complete. In 1985, Jean-Pierre Serre proposed that a Frey curve could not be modular and provided a partial proof of this. This showed that a proof of the semistable case of the Taniyama-Shimura conjecture would imply Fermat's Last Theorem. Serre did not provide a complete proof and what was missing became known as the [[epsilon conjecture]] or ε-conjecture. In the summer of 1986, Ribet (1990) proved the epsilon conjecture, thereby proving that the Taniyama–Shimura–Weil conjecture implied Fermat's Last Theorem.

			==References==

			*{{Citation \| last1=Frey \| first1=Gerhard \| title=Links between stable elliptic curves and certain Diophantine equations \| mr=853387 \| year=1986 \| journal=Annales Universitatis Saraviensis. Series Mathematicae \| issn=0933-8268 \| volume=1 \| issue=1 \| pages=iv+40}}
			*{{Citation \| last1=Frey \| first1=Gerhard \| title=Rationale Punkte auf Fermatkurven und getwisteten Modulkurven\| year=1982 \| journal=J.reine u.angew.Math \| volume=331 \| pages=185–191}}
			*{{Citation \| last1=Hellegouarch \| first1=Yves \| title=Rectificatif à l'article de H. Darmon intitulé : "La Conjecture de Shimura-Taniyama-Weil est enfin démontré" \| url=http://www.math.unicaen.fr/~nitaj/hellegouarch.html \| year=2000 \| journal=Gazette des Mathématiciens \| issn=0224-8999 \| volume=83}}
			*{{Citation \| last1=Hellegouarch \| first1=Yves \| title=Points d'ordre 2p<sup>h</sup> sur les courbes elliptiques \| url=http://matwbn.icm.edu.pl/tresc.php?wyd=6&tom=26 \| mr=0379507 \| year=1974 \| journal=Polska Akademia Nauk. Instytut Matematyczny. Acta Arithmetica \| issn=0065-1036 \| volume=26 \| issue=3 \| pages=253–263}}
			*{{Citation \| last1=Hellegouarch \| first1=Yves \| title=Invitation to the mathematics of Fermat-Wiles \| publisher=[[Academic Press]] \| location=Boston, MA \| isbn=978-0-12-339251-0 \| mr=1475927 \| year=2002}}

			[[Category:Number theory]]

en>EmilJ: Undid revision 510123169 by 141.23.65.251 (talk) What is that supposed to mean?

2012-08-31T15:39:24Z

Undid revision 510123169 by 141.23.65.251 (talk) What is that supposed to mean?

New page

Claude is her title and she completely digs that name. My home is now in Kansas. The preferred pastime for my kids and me is dancing and now I'm attempting to make cash with it. Managing people is what I do in my day job.<br><br>Feel free to visit my website; [http://sceltic.at/index.php?mod=users&action=view&id=51301 http://sceltic.at/index.php?mod=users&action=view&id=51301]