### Abstract

If b(m;n) denotes the number of partitions of n into powers of m, then b(m; m^{r+1}n) ≡ b(m; m^{r}n) (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) |
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Pages (from-to) | 104-110 |

Number of pages | 7 |

Journal | Journal of Number Theory |

Volume | 3 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 1971 |

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### All Science Journal Classification (ASJC) codes

- Algebra and Number Theory

### Cite this

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*Journal of Number Theory*, vol. 3, no. 1, pp. 104-110. https://doi.org/10.1016/0022-314X(71)90051-5

**Congruence properties of the m-ary partition function.** / Andrews, George E.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Congruence properties of the m-ary partition function

AU - Andrews, George E.

PY - 1971/1/1

Y1 - 1971/1/1

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.

UR - http://www.scopus.com/inward/record.url?scp=0007153044&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0007153044&partnerID=8YFLogxK

U2 - 10.1016/0022-314X(71)90051-5

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

M3 - Article

VL - 3

SP - 104

EP - 110

JO - Journal of Number Theory

JF - Journal of Number Theory

SN - 0022-314X

IS - 1

ER -