A complete formalization of Fermat's Last Theorem for regular primes in Lean
Formal Languages and Automata Theory
2025-06-16 v3 Logic in Computer Science
Number Theory
Abstract
We formalize a complete proof of the regular case of Fermat's Last Theorem in the Lean4 theorem prover. Our formalization includes a proof of Kummer's lemma, that is the main obstruction to Fermat's Last Theorem for regular primes. Rather than following the modern proof of Kummer's lemma via class field theory, we prove it by using Hilbert's Theorems 90-94 in a way that is more amenable to formalization.
Cite
@article{arxiv.2410.01466,
title = {A complete formalization of Fermat's Last Theorem for regular primes in Lean},
author = {Alex Best and Christopher Birkbeck and Riccardo Brasca and Eric Rodriguez Boidi and Ruben van De Velde and Andrew Yang},
journal= {arXiv preprint arXiv:2410.01466},
year = {2025}
}