Diophantus' 20th Problem and Fermat's Last Theorem for n=4: Formalization of Fermat's Proofs in the Coq Proof Assistant - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2005

Diophantus' 20th Problem and Fermat's Last Theorem for n=4: Formalization of Fermat's Proofs in the Coq Proof Assistant

Résumé

We present the proof of Diophantus' 20th problem (book VI of Diophantus' Arithmetica), which consists in wondering if there exist right triangles whose sides may be measured as integers and whose surface may be a square. This problem was negatively solved by Fermat in the 17th century, who used the "wonderful" method (ipse dixit Fermat) of infinite descent. This method, which is, historically, the first use of induction, consists in producing smaller and smaller non-negative integer solutions assuming that one exists; this naturally leads to a reductio ad absurdum reasoning because we are bounded by zero. We describe the formalization of this proof which has been carried out in the Coq proof assistant. Moreover, as a direct and no less historical application, we also provide the proof (by Fermat) of Fermat's last theorem for n=4, as well as the corresponding formalization made in Coq.
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Dates et versions

hal-00009425 , version 1 (03-10-2005)

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David Delahaye, Micaela Mayero. Diophantus' 20th Problem and Fermat's Last Theorem for n=4: Formalization of Fermat's Proofs in the Coq Proof Assistant. 2005. ⟨hal-00009425⟩
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