Congruences modulo powers of 5 for partitions into odd and distinct parts

Abstract

Let Q ₀(n) denote the number of partitions of n into odd and distinct parts. In 1969, Rødseth proved an infinite family of congruences modulo high powers of 5 for Q ₀(n) by employing the theory of modular forms. In this paper, we not only provide a completely elementary proof of the congruence family due to Rødseth, but also establish two another congruence families modulo high powers of 5 satisfied by Q ₀(n).