# Formal verification of Zagier's one-sentence proof

Dubach G, Mühlböck F. Formal verification of Zagier’s one-sentence proof. arXiv, 2103.11389.

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Abstract

We comment on two formal proofs of Fermat's sum of two squares theorem, written using the Mathematical Components libraries of the Coq proof assistant. The first one follows Zagier's celebrated one-sentence proof; the second follows David Christopher's recent new proof relying on partition-theoretic arguments. Both formal proofs rely on a general property of involutions of finite sets, of independent interest. The proof technique consists for the most part of automating recurrent tasks (such as case distinctions and computations on natural numbers) via ad hoc tactics.

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Date Published

2021-03-21

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arXiv

Article Number

2103.11389

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### Cite this

Dubach G, Mühlböck F. Formal verification of Zagier’s one-sentence proof.

*arXiv*.Dubach, G., & Mühlböck, F. (n.d.). Formal verification of Zagier’s one-sentence proof.

*arXiv*.Dubach, Guillaume, and Fabian Mühlböck. “Formal Verification of Zagier’s One-Sentence Proof.”

*ArXiv*, n.d.G. Dubach and F. Mühlböck, “Formal verification of Zagier’s one-sentence proof,”

*arXiv*. .Dubach G, Mühlböck F. Formal verification of Zagier’s one-sentence proof. arXiv, 2103.11389.

Dubach, Guillaume, and Fabian Mühlböck. “Formal Verification of Zagier’s One-Sentence Proof.”

*ArXiv*, 2103.11389.**All files available under the following license(s):**

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arXiv 2103.11389