Congruence properties of the m-ary partition function

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Abstract

If b(m;n) denotes the number of partitions of n into powers of m, then b(m; mr+1n) ≡ b(m; mrn) (mod μr) where μ = m if m is odd and μ = m 2 if m is even. The existence of such a congruence was conjectured by R. F. Churchhouse and its truth for m a prime was proved by O. Rödseth.

Original languageEnglish (US)
Pages (from-to)104-110
Number of pages7
JournalJournal of Number Theory
Volume3
Issue number1
DOIs
StatePublished - Feb 1971

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All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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