2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/58734Let m be a positive integer, and let A be the set of all positive integers that belong to a union of r distinct congruence classes modulo m. We assume that the elements of A are relatively prime, that is, gcd(A) = 1. Let p_A(n) denote the number of partitions of n into parts belonging to A. We obtain the asymptotic formula log p_A(n) ~ π\sqrt(2rn/3m). The proof is based on Erdos's elementary method to obtain the asymptotic formula for the usual partition function p(n).14 pages. To appear in the proceedings of the conference "Paul Erdos and his Mathematics," which was held in Budapest in July,1999Number TheoryCombinatoricsPrimary 11P81,11P82. Secondary 11B05,11B75text