Fermat equation
From Encyclopedia of Mathematics
The printable version is no longer supported and may have rendering errors. Please update your browser bookmarks and please use the default browser print function instead.
The Diophantine equation $x^n+y^n=z^n$, $n\in \mathbb N$, $x,y\in \mathbb Z$, of which it was fairly recently proved (in 1995) that there are no non-trivial solutions if $n\geq3$ (see, e.g., [a1]).
See Fermat great theorem for an account of affairs before A. Wiles' recent proof [a3].
See Fermat last theorem and [a1] for a sketch of the basic ideas and techniques behind the proof. See also [a1] for related matters such as the generalized Fermat conjecture and the Fermat equation over function fields; see also [a2].
References
[a1] | A.J. van der Poorten, "Notes on Fermat's last theorem" , Wiley (1996) |
[a2] | L. Denis, "Le théorème de Fermat–Goss" Trans. Amer. Math. Soc. , 343 (1994) pp. 713–726 |
[a3] | A. Wiles, "Modular elliptic curves and Fermat's last theorem" Ann. of Math. , 141 (1995) pp. 443–551 |
How to Cite This Entry:
Fermat equation. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Fermat_equation&oldid=29132
Fermat equation. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Fermat_equation&oldid=29132
This article was adapted from an original article by M. Hazewinkel (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article