A note on Fermat's Last Theorem for $n=4$

Matan Eliashar; Nati Linial

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arXiv · 2302.02378

A note on Fermat's Last Theorem for $n=4$

Matan Eliashar·Nati Linial

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Abstract

Fermat's Last theorem (FLT) famously states that the equation $x^n+y^n=z^n$ has no solution in positive integers $x, y, z$ for any integer exponent $n>2$. But does this theorem have a quantitative version? Upon initial investigation we discovered an infinite sequence of integers $(x_n, y_n, z_n)$ with $x_n^4+y_n^4-8=z_n^2$.

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Matan Eliashar, Nati Linial. 2023-02-05. A note on Fermat's Last Theorem for $n=4$. https://arxiv.org/abs/2302.02378

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