Sur le théorème de Fermat sur Q(√5)

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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 Q(√5) for the exponent p. It is related to the Wendt's resultant of the polynomials Xⁿ-1 and (X+1)ⁿ-1. We deduce Fermat's Last Theorem over this field in case one has 5≤ p<10⁷, and we obtain analogous results on Sophie Germain type criteria.