An extension of a congruence by Andrews for generalized frobenius partitions

AbstractIn a recent paper George E. Andrews introduced the idea of generalized Frobenius partitions. In his paper Andrews showed that cφm(n), the number of generalized Frobenius partitions of n with m colors, satisfies the congruence cφp(n)=0 (mod p2 if p∤ncφ1(np) (mod p2) if p|n where p is a prime, using a purely combinatorial argument. In this paper we will show how this congruence when viewed in a slightly different form can be extended to cφm(n) for all positive values of m