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

2023/02/05 by Eliashar, Matan, Linial, Nati · 1 citation
#FOS: Mathematics #General Mathematics (math.GM)

paper · doi:10.48550/arxiv.2302.02378

Abstract

Fermat's Last theorem (FLT) famously states that the equation xⁿ+yⁿ=zⁿ 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_n⁴+y_n⁴-8=z_n².

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