Beyond and slightly aside of the Fermat Desert
Boris Bartolom\'e, Preda Mihailescu

TL;DR
This paper provides a cyclotomic proof that certain equations involving prime exponents have no solutions in coprime integers, thereby supporting Fermat's Last Theorem.
Contribution
It introduces a cyclotomic approach to prove the non-existence of solutions for a specific class of equations related to Fermat's Last Theorem.
Findings
Proves the equation has no solutions for prime p > 3 in coprime integers.
Establishes a cyclotomic proof technique for related exponential equations.
Supports Fermat's Last Theorem through this specific case.
Abstract
We give a cyclotomic proof of the fact that the equation has no solutions in coprime integers and , a prime. This implies in particular Fermat's Last Theorem.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · History and Theory of Mathematics · Mathematical Dynamics and Fractals
