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Fermat's Last Theorem for regular primes

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arxiv 2305.08955 v2 pith:YIIQOQMV submitted 2023-05-15 cs.LO math.NT

Fermat's Last Theorem for regular primes

classification cs.LO math.NT
keywords emphtheoremfermatfieldslastmathlibnumberprimes
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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We formalise the proof of the first case of Fermat's Last Theorem for regular primes using the \emph{Lean} theorem prover and its mathematical library \emph{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 \emph{mathlib}.

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