The asymptotic Fermat’s Last Theorem for five-sixths of real quadratic fields
The asymptotic Fermat’s Last Theorem for five-sixths of real quadratic fields
Let $K$ be a totally real field. By the asymptotic Fermat’s Last Theorem over $K$ we mean the statement that there is a constant $B_{K}$ such that for any prime exponent $p>B_{K}$ , the only solutions to the Fermat equation $$\begin{eqnarray}a^{p}+b^{p}+c^{p}=0,\quad a,b,c\in K\end{eqnarray}$$ are the trivial ones satisfying $abc=0$ . …