More on Divisibility Criteria for Selected Primes

Adam Naumowicz; Radosław Piliszek

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On $D$ sot hat $x^{2} - D y^{2}$ represents $m$ and $- m$ and not $- 1$ .

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This article provides a formalized proof of the so-called “the four-square theorem”, namely any natural number can be expressed by a sum of four squares, which was proved by Lagrange in 1770. An informal proof of the theorem can be found in the number theory literature, e.g. in [14], [1] or [23]. This theorem is item #19 from the “Formalizing 100 Theorems” list maintained by Freek Wiedijk at http://www.cs.ru.nl/F.Wiedijk/100/.

On $D$ so that $x^{2} - D y^{2} = \pm m$ .

Robertson, John P. (2006)

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