On m–ary Partition Function Congruences: A Fresh Look at a Past Problem

Abstract

Let bm(n) denote the number of partitions of n into powers of m. Define σr = ε2m 2 + ε3m 3 + · · · + εrm, where εi = 0 or 1 for each i. Moreover, let cr = 1 if m is odd, and cr = 2 r−1 if m is even. The main goal of this paper is to prove the congruence bm(m n− σr −m) ≡ 0 (mod m/cr). For σr = 0, the existence of such a congruence was conjectured by R. F… (More)

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Cite this paper

@inproceedings{Sellers2001OnMP, title={On m–ary Partition Function Congruences: A Fresh Look at a Past Problem}, author={James A. Sellers}, year={2001} }