Fermat's theorem on Q (root 5)

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