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Zbl 0586.10010
Frey, Gerhard
Links between stable elliptic curves and certain diophantine equations. (English)
[J] Ann. Univ. Sarav., Ser. Math. 1, No.1, 40 p. (1986). ISSN 0933-8268

The paper under review relates solutions of the Fermat equation $X\sp p+Y\sp p=Z\sp p$ to elliptic curves. To (x,y,z) corresponds the elliptic curve $U\sp 2=V(V-x\sp p)(V-z\sp p).$ He then shows that this elliptic curve has many remarkable properties, so that one might hope to show that it does not exist. He explains several approaches on how to do this, which lead to quite plausible conjectures which would imply Fermat's Last Theorem.
[G.Faltings]

MSC 2000:: *11D41 Higher degree diophantine equations
14H52 Elliptic curves

Keywords: Fermat equation; elliptic curves; Fermat's Last Theorem

Cited in: Zbl 0969.11023 Zbl 0816.11023 Zbl 0811.11024 Zbl 0773.11039 Zbl 0706.14015 Zbl 0641.10026

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