Sur le théorème de Fermat sur $\mathbf{Q}(\sqrt{5})$

Abstract

Let $p$ be an odd prime number. Using modular arguments, we give an easy testable condition which allows often to prove Fermat's Last Theorem over the quadratic field $\mathbf{Q}(\sqrt{5})$ for the exponent $p$. It is related to the Wendt's resultant of the polynomials $X^n-1$ and $(X+1{)}^n-1$. We deduce Fermat's Last Theorem over this field in case one has $5\le p<10^7$, and we obtain analogous results on Sophie Germain type criteria.

in French