Report
Formal verification of Zagier's one-sentence proof
| العنوان: | Formal verification of Zagier's one-sentence proof |
|---|---|
| المؤلفون: | Dubach, Guillaume, Muehlboeck, Fabian |
| سنة النشر: | 2021 |
| المجموعة: | Computer Science Mathematics |
| مصطلحات موضوعية: | Computer Science - Logic in Computer Science, Mathematics - Number Theory, 68V15 (Primary) 68V20, 11P81 (Secondary) |
| الوصف: | 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 more recent 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. With the same method, we also provide a formal proof of another classical result on primes of the form $a^2 + 2 b^2$. Comment: 13 pages, 6 figures |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2103.11389 |
| رقم الانضمام: | edsarx.2103.11389 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |