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arXiv · 2607.19420

Theorems Related to Fermat's Sums of Two Squares

Francois Wolf·Marc Wolf
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Abstract

In this paper, we study the factorization of sums of two squares X2 + Y2. We show the existence of linear and quadratic progressions on X that generate both factorizations and alternative decompositions into sums of two squares. We are therefore naturally interested in the number of decompositions into sums of two squares of an integer n and relate it to its number of divisors d(n). Finally, we present an algorithm to obtain these decompositions using the sieve introduced in (1).

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Francois Wolf, Marc Wolf. 2026-07-19. Theorems Related to Fermat's Sums of Two Squares. https://arxiv.org/abs/2607.19420

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