✦ LIBER ✦
On m-ary Partition Function Congruences: A Fresh Look at a Past Problem
✍ Scribed by Øystein J. Rødseth; James A. Sellers
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 110 KB
- Volume
- 87
- Category
- Article
- ISSN
- 0022-314X
No coin nor oath required. For personal study only.
✦ Synopsis
Let b m (n) denote the number of partitions of n into powers of m. Define _ r = = 2 m 2 += 3 m 3 + } } } += r m r , where = i =0 or 1 for each i. Moreover, let c r =1 if m is odd, and c r =2 r&1 if m is even. The main goal of this paper is to prove the congruence b m (m r+1 n&_ r &m)#0 (mod m r Âc r ). For _ r =0, the existence of such a congruence was conjectured by R. F. Churchhouse some 30 years ago, and its truth was proved by O 3 . J. Ro % dseth, G. E. Andrews, and H. Gupta soon after.