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On m-ary partitions

Published online by Cambridge University Press:  24 October 2008

Hansraj Gupta
Hansraj Gupta
Affiliation:
Allahabad University, Allahabad, India
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Extract

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.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 71 , Issue 2 , March 1972 , pp. 343 - 345
Copyright
Copyright © Cambridge Philosophical Society 1972

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References

REFERENCES

(1)Churchhouse, R. F.Congruence properties of the binary partition function. Proc. Cambridge Philos. Soc. 66 (1969), 371–376.CrossRefGoogle Scholar
(2)Andrews, G. E.Congruence properties of the m-ary partition function. J. Number Theory 3 (1971), 104–110.CrossRefGoogle Scholar