Congruence properties of the m-ary partition function

Research output: Contribution to journalArticle

22 Citations (Scopus)

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 - Jan 1 1971

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Partition Function
Congruence
Odd
Partition
Denote
Truth

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

Cite this

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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. R{\"o}dseth.",
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Congruence properties of the m-ary partition function. / Andrews, George E.

In: Journal of Number Theory, Vol. 3, No. 1, 01.01.1971, p. 104-110.

Research output: Contribution to journalArticle

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