### 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 - Feb 1971 |

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### All Science Journal Classification (ASJC) codes

- Algebra and Number Theory