Sur le théorème de Fermat sur $${\mathbb Q}\big (\sqrt{5}\big )$$
Tóm tắt
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
$${\mathbb Q}\bigl (\sqrt{5}\bigr )$$
for the exponent p. It is related to Wendt’s resultant of the polynomials
$$X^n-1$$
and
$$(X+1)^n-1$$
. We deduce Fermat’s Last Theorem over this field for p in case one has
$$5\le p<10^7$$
, and we obtain results analogous to Sophie Germain type criteria.
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