On m-ary partition function congruences: A fresh look at a past problem

Øystein J. Rødseth, James A. Sellers

Research output: Contribution to journalArticlepeer-review

20 Scopus citations

Abstract

Let bm(n) denote the number of partitions of n into powers of m. Define σr2m23m3+...+εrmr, where εi=0 or 1 for each i. Moreover, let cr=1 if m is odd, and cr=2r-1 if m is even. The main goal of this paper is to prove the congruence bm(mr+1n-σr-m)≡0 (modmr/cr). For σr=0, the existence of such a congruence was conjectured by R. F. Churchhouse some 30 years ago, and its truth was proved by Ø. J. Rødseth, G. E. Andrews, and H. Gupta soon after.

Original languageEnglish (US)
Pages (from-to)270-281
Number of pages12
JournalJournal of Number Theory
Volume87
Issue number2
DOIs
StatePublished - Apr 2001

Keywords

  • Congruences
  • Partitions

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