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On m-ary partitions

  • Hansraj Gupta (a1)

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1. Let g(n) = g(n; m) denote the number of partitions of a natural number n into powers of a given natural number m (> 2). Then the generating function of g(n) is

(1) where we take g(0) = 1.

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References

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(1)Churchhouse, R. F.Congruence properties of the binary partition function. Proc. Cambridge Philos. Soc. 66 (1969), 371376.
(2)Andrews, G. E.Congruence properties of the m-ary partition function. J. Number Theory 3 (1971), 104110.
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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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