Abstract
Let bm(n) denote the number of partitions of n into powers of m. Define σr=ε2m2+ε3m3+...+εrmr, where εi=0 or 1 for each i. Moreover, let cr=1 if m is odd, and cr=2r-1 if m is even. The main goal of this paper is to prove the congruence bm(mr+1n-σr-m)≡0 (modmr/cr). For σr=0, the existence of such a congruence was conjectured by R. F. Churchhouse some 30 years ago, and its truth was proved by Ø. J. Rødseth, G. E. Andrews, and H. Gupta soon after.
Original language | English (US) |
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Pages (from-to) | 270-281 |
Number of pages | 12 |
Journal | Journal of Number Theory |
Volume | 87 |
Issue number | 2 |
DOIs | |
State | Published - Apr 2001 |
Externally published | Yes |
Keywords
- Congruences
- Partitions