The strong Fermat-Catalan Equation

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

paper · pdf · doi:10.48550/arxiv.2509.18275

openalex publication_date 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

Related

• Beyond and slightly aside of the Fermat Desert
• A Cylcotomic Investigation of the Fermat - Catalan Equation
• On Fermat's Last Theorem for odd prime exponents
• Catalan's Equation For Even Primes over Quadratic Fields
• Fermat's Equation Has No Solution with Some Prime Components