2026/07/19 by Francois Wolf, Marc Wolf
#math.GM
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).