文摘
The notion of broken k -diamond partitions was introduced by Andrews and Paule. Let 74095ec4d0b370bb513ecfed5bed3613" title="Click to view the MathML source">Δk(n) denote the number of broken k-diamond partitions of n for a fixed positive integer k . Recently, Chan, and Paule and Radu proved some congruences modulo 5 for 728e0ddd116abb" title="Click to view the MathML source">Δ2(n). In this paper, we prove several new infinite families of congruences modulo 5 for 728e0ddd116abb" title="Click to view the MathML source">Δ2(n) by using an identity due to Newman. Our results generalize the congruences proved by Paule and Radu.