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A complete formalization of Fermat's Last Theorem for regular primes in Lean
cs.FL
Oct 2, 2024 · v1
TL;DR
Formalizes a complete proof of Fermat's Last Theorem for regular primes in Lean 4.
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, the main obstruction to Fermat's Last Theorem for regular primes. Instead of using the modern approach via class field theory, we prove it by using Hilbert's Theorems 90-94 in a way that is more amenable to formalization.
Problem
Fermat's Last Theorem for regular primes is a major number-theoretic result whose formalization in a proof assistant had not been completed, particularly due to the difficulty of Kummer's lemma.
Approach
The authors formalize the complete proof of the regular case of Fermat's Last Theorem in Lean 4. Rather than using the modern approach via class field theory, they prove Kummer's lemma using Hilbert's Theorems 90-94, which is more amenable to formalization in a proof assistant.
Results
The formalization is complete and includes a full proof of Kummer's lemma, the main obstruction to Fermat's Last Theorem for regular primes, verified by Lean 4's kernel.