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Acta Mathematica Vietnamica

Congruences for Partition Quadruples with t-Cores

icon-email M. S. Mahadeva Naika , S. Shivaprasada Nayaka

Abstract

Let Ct(n) denote the number of partition quadruples of n with t-cores for t=3,5,7,25. We establish some Ramanujan type congruences modulo 5,7,8 for Ct(n). For example, n0, we have C5(5n+4)0(mod5),C7(7n+6)0(mod7),C3(16n+14)0(mod8).