  Let 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) ~ \pi \sqrt(2rn/3m). The proof is based on
Erdos's elementary method to obtain the asymptotic formula for the usual
partition function p(n).
