CONGRUENCES MODULO 5 AND 7 FOR 4-COLORED GENERALIZED FROBENIUS PARTITIONS

Abstract

Let c phi(k)(n) denote the number of k-colored generalized Frobenius partitions of n. Recently, new Ramanujan-type congruences associated with c phi(4)(n) were discovered. In this article, we discuss two approaches in proving such congruences using the theory of modular forms. Our methods allow us to prove congruences such as c phi(4)(14n + 6) 0 mod 7 and Seller's congruence c phi(4)(10n + 6) 0 mod 5.