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The notion of broken k-diamond partitions was introduced by Andrews and Paule. Let $$\Delta _k(n)$$ Δ k ( n ) denote the number of broken k-diamond partitions of n for a fixed positive integer k. Recently, a number of parity results satisfied by $$\Delta _k(n)$$ Δ k ( n ) for small values of k have been proved by Radu and Sellers and others. However, congruences modulo...
The notion of broken k-diamond partitions was introduced by Andrews and Paule in 2007. For a fixed positive integer k, let $$\Delta _k(n)$$ Δk(n) denote the number of broken k-diamond partitions of n. Recently, Paule and Radu conjectured two relations on $$\Delta _5(n)$$ Δ5(n) which were proved by Xiong and Jameson, respectively. In this paper, employing these relations, we prove that, for any prime...
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