On Fermat curves modulo a finite number

2017/07/03 by Yochay Jerby, Jerby, Yochay
Mathematics · #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #General Mathematics (math.GM) #History and Theory of Mathematics #math.GM

paper · pdf · doi:10.48550/arxiv.1707.01856

openalex publication_date 2017/07/03 · arxiv created 2017/08/10 · arxiv updated 2017/08/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the existence of a non-trivial solution of xⁿ+yⁿ=pⁿ, with p a prime number, is equivalent to the existence of a solution of a certain (over-determined) system of (n-1)-recursion relations ("zipper" equations) in ℤ_p-1.

Citations

• Modular Elliptic Curves and Fermat's Last Theorem

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