19/12/29 23:08:10.15 uR3g5aDb.net
>>765
>>765
この日本文は不正確
正確には、下記英文
なお、下記(a, b, c, n)は (a, b, c, p)が正確かもね、y^2 = x (x - a^p)(x + b^p)だからね
URLﾘﾝｸ(en.wikipedia.org)
Fermat's Last Theorem
(抜粋)
Contents
2.5 Connection with elliptic curves
Ribet's theorem for Frey curves
Main articles: Frey curve and Ribet's theorem
In 1984, Gerhard Frey noted a link between Fermat's equation and the modularity theorem, then still a conjecture.
If Fermat's equation had any solution (a, b, c) for exponent p > 2, then it could be shown that the semi-stable elliptic curve (now known as a Frey-Hellegouarch[note 3])
y^2 = x (x - a^p)(x + b^p)
would have such unusual properties that it was unlikely to be modular.[122]
This would conflict with the modularity theorem, which asserted that all elliptic curves are modular.
As such, Frey observed that a proof of the Taniyama?Shimura?Weil conjecture might also simultaneously prove Fermat's Last Theorem.[123]
By contraposition, a disproof or refutation of Fermat's Last Theorem would disprove the Taniyama?Shimura?Weil conjecture.
In plain English, Frey had shown that, if this intuition about his equation was correct, then any set of 4 numbers (a, b, c, n) capable of disproving Fermat's Last Theorem, could also be used to disprove the Taniyama?Shimura?Weil conjecture.
Therefore if the latter were true, the former could not be disproven, and would also have to be true.
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