# Fermat equation

From Encyclopedia of Mathematics

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

This article was adapted from an original article by M. Hazewinkel (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article