Congruence properties of the m-ary partition function

George E. Andrews

doi:10.1016/0022-314X(71)90051-5

Congruence properties of the m-ary partition function

George E. Andrews

Mathematics

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29 Scopus citations

Abstract

If b(m;n) denotes the number of partitions of n into powers of m, then b(m; m^r+1n) ≡ b(m; m^rn) (mod μ^r) 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 language	English (US)
Pages (from-to)	104-110
Number of pages	7
Journal	Journal of Number Theory
Volume	3
Issue number	1
DOIs	https://doi.org/10.1016/0022-314X(71)90051-5
State	Published - Feb 1971

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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10.1016/0022-314X(71)90051-5

Cite this

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title = "Congruence properties of the m-ary partition function",

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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N2 - 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.

AB - 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.

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DO - 10.1016/0022-314X(71)90051-5

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AN - SCOPUS:0007153044

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SP - 104

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JO - Journal of Number Theory

JF - Journal of Number Theory

IS - 1

ER -

Congruence properties of the m-ary partition function

Abstract

All Science Journal Classification (ASJC) codes

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