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

General Mathematics 2023-02-07 v1

Abstract

Fermat's Last theorem (FLT) famously states that the equation xn+yn=znx^n+y^n=z^n has no solution in positive integers x,y,zx, y, z for any integer exponent n>2n>2. But does this theorem have a quantitative version? Upon initial investigation we discovered an infinite sequence of integers (xn,yn,zn)(x_n, y_n, z_n) with xn4+yn48=zn2x_n^4+y_n^4-8=z_n^2.

Cite

@article{arxiv.2302.02378,
  title  = {A note on Fermat's Last Theorem for $n=4$},
  author = {Matan Eliashar and Nati Linial},
  journal= {arXiv preprint arXiv:2302.02378},
  year   = {2023}
}
R2 v1 2026-06-28T08:32:20.945Z