A complete formalization of Fermat's Last Theorem for regular primes in Lean
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911003933933568 |
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| author | Best, Alex Birkbeck, Christopher Brasca, Riccardo Boidi, Eric Rodriguez van De Velde, Ruben Yang, Andrew |
| author_facet | Best, Alex Birkbeck, Christopher Brasca, Riccardo Boidi, Eric Rodriguez van De Velde, Ruben Yang, Andrew |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_01466 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A complete formalization of Fermat's Last Theorem for regular primes in Lean Best, Alex Birkbeck, Christopher Brasca, Riccardo Boidi, Eric Rodriguez van De Velde, Ruben Yang, Andrew Formal Languages and Automata Theory Logic in Computer Science Number Theory 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. |
| title | A complete formalization of Fermat's Last Theorem for regular primes in Lean |
| topic | Formal Languages and Automata Theory Logic in Computer Science Number Theory |
| url | https://arxiv.org/abs/2410.01466 |