The strong Fermat-Catalan Equation

2025/09/22 by Preda Mihăilescu, Preda Mihailescu, Mihailescu, Preda · 1 voice
Computer Science · Mathematics · #FOS: Mathematics #History and Theory of Mathematics #Mathematical and Theoretical Analysis #Number Theory (math.NT) #Polynomial and algebraic computation #math.NT

paper · pdf · doi:10.48550/arxiv.2509.18275

openalex publication_date 2025/09/22 · arxiv published 2025/09/22 · arxiv updated 2025/09/22 · openalex created_date 2025/10/16 · openalex updated_date 2026/07/28

Abstract

We give a cyclotomic proof of the fact that the equation (x^p + y^p)/(x+y) = p^e z^q has no solutions in coprime integers x,y,z and p > 3; q, a pair of distinct odd primes.

Citations

• Modular Elliptic Curves and Fermat's Last Theorem

Discussions

• The strong Fermat-Catalan Equation - By arXiv:2509.18275v1 https://arxiv.org/abs/2509.18275 A cyclotomic proof shows no solutions exist for the equation (x^p + y^p)/(x+y) = p^e z^q in coprime integers [bsky, 0 points, 0 comments]

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