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Communication Dans Un Congrès Année : 2023

Fermat’s Last Theorem for Regular Primes (Short Paper)

Alex Best
Christopher Birkbeck
Eric Rodriguez Boidi

Résumé

We formalise the proof of the first case of Fermat’s Last Theorem for regular primes using the Lean theorem prover and its mathematical library mathlib. This is an important 19th century result that motivated the development of modern algebraic number theory. Besides explaining the mathematics behind this result, we analyze in this paper the difficulties we faced in the formalisation process and how we solved them. For example, we had to deal with a diamond about characteristic zero fields and problems arising from multiple nested coercions related to number fields. We also explain how we integrated our work to mathlib.

Dates et versions

hal-04464277 , version 1 (18-02-2024)

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Alex Best, Christopher Birkbeck, Riccardo Brasca, Eric Rodriguez Boidi. Fermat’s Last Theorem for Regular Primes (Short Paper). International Conference on Interactive Theorem Proving (ITP), Jul 2023, Białystok, Poland. ⟨10.4230/LIPIcs.ITP.2023.36⟩. ⟨hal-04464277⟩
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