A complete formalization of Fermat's Last Theorem for regular primes in Lean

TL;DR

This paper presents a formal proof of the regular case of Fermat's Last Theorem in Lean4, emphasizing a novel approach to proving Kummer's lemma using Hilbert's theorems for better formalization.

Contribution

It provides the first complete formalization of the regular case of Fermat's Last Theorem in Lean4, including a new proof of Kummer's lemma using Hilbert's theorems.

Findings

Formal proof of Fermat's Last Theorem for regular primes in Lean4

Novel proof of Kummer's lemma using Hilbert's theorems 90-94

Enhanced formalization approach for algebraic number theory theorems

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.