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

Authors Alex J. Best , Christopher Birkbeck , Riccardo Brasca , Eric Rodriguez Boidi



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Author Details

Alex J. Best
  • King’s College London, UK
Christopher Birkbeck
  • University of East Anglia, Norwich, UK
Riccardo Brasca
  • Université Paris Cité, France
Eric Rodriguez Boidi
  • King’s College London, UK

Acknowledgements

We thank the mathlib community for a lot of useful discussions around our project. We especially thank Ruben Van de Velde for having formalised in Lean a proof of Fermat’s Last Theorem in the case n = 3.

Cite AsGet BibTex

Alex J. Best, Christopher Birkbeck, Riccardo Brasca, and Eric Rodriguez Boidi. Fermat’s Last Theorem for Regular Primes (Short Paper). In 14th International Conference on Interactive Theorem Proving (ITP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 268, pp. 36:1-36:8, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
https://doi.org/10.4230/LIPIcs.ITP.2023.36

Abstract

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.

Subject Classification

ACM Subject Classification
  • General and reference → Verification
  • Computing methodologies → Representation of mathematical objects
  • Mathematics of computing → Mathematical software
Keywords
  • Fermat’s Last Theorem
  • Cyclotomic fields
  • Interactive theorem proving
  • Lean

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