TY - JOUR
T1 - On m-ary partition function congruences
T2 - A fresh look at a past problem
AU - Rødseth, Øystein J.
AU - Sellers, James A.
PY - 2001/4
Y1 - 2001/4
N2 - 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.
AB - 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.
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U2 - 10.1006/jnth.2000.2594
DO - 10.1006/jnth.2000.2594
M3 - Article
AN - SCOPUS:18044372222
SN - 0022-314X
VL - 87
SP - 270
EP - 281
JO - Journal of Number Theory
JF - Journal of Number Theory
IS - 2
ER -