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arXiv · 1710.10163

On Fermat's equation over some quadratic imaginary number fields

George Turcas
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Abstract

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 all prime exponents $p \geq 5$, Fermat's equation $a^p+b^p+c^p=0$ does not have non-trivial solutions over $\mathbb Q(\sqrt{-2})$ and $\mathbb Q(\sqrt{-7})$.

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George Turcas. 2017-10-25. On Fermat's equation over some quadratic imaginary number fields. https://doi.org/10.1007/s40993-018-0117-y

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