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Congruence properties of the binary partition function

Published online by Cambridge University Press:  24 October 2008

M. D. Hirschhorn  and
J. H. Loxton
M. D. Hirschhorn
Affiliation:
School of Mathematics, University of New South Wales, Kensington, N. S. W., Australia
J. H. Loxton
Affiliation:
School of Mathematics, University of New South Wales, Kensington, N. S. W., Australia
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Extract

We denote by b(n) the number of binary partitions of n, that is the number of partitions of n as the sum of powers of 2. As usual, two partitions are not considered to be distinct if they differ only in the order of their summands. It is convenient to define b(0) = 1.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 78 , Issue 3 , November 1975 , pp. 437 - 442
Copyright
Copyright © Cambridge Philosophical Society 1975

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References

REFERENCES

(1)Churchhouse, R. F.Congruences for the binary partition function. Proc. Cambridge Philos. Soc. 66 (1969), 371–376.CrossRefGoogle Scholar
(2)Gupta, H.Proof of the Churchhouse conjecture concerning binary partitions. Proc. Cambridge Philos. Soc. 70 (1971), 53–56.CrossRefGoogle Scholar
(3)RÖdseth, Ö.Some arithmetical properties of m-ary partitions. Proc. Cambridge Philos. Soc. 68 (1970), 447–453.CrossRefGoogle Scholar