Assuming a deep but standard conjecture in the Langlands programme, we prove Fermat's Last Theorem over $\mathbb Q(i)$. Under the same assumption, we also prove that for $p \geq 5$, Fermat's Equation with prime exponent $a^p+b^p+c^p=0$ does not have non-trivial solutions over $\mathbb Q(i), \mathbb Q(\sqrt{-2})$ and $\mathbb Q(\sqrt{-7})$. 查看全文>>