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Link to this article: http://journals.cambridge.org/abstract_S0305004100046259How to cite this article: Öystein Rödseth (1970). Some arithmetical properties of m-ary partitions. Mathematical

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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. 2001Academic Press

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