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Congruence properties of the binary partition function

Published online by Cambridge University Press:  24 October 2008

R. F. Churchhouse
R. F. Churchhouse
Affiliation:
Atlas Computer Laboratory, Chilton, Didcot, Berks.
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Extract

We denote by b(n) the number of ways of expressing the positive integer n as the sum of powers of 2 and we call b(n) ‘the binary partition function’. This function has been studied by Euler (1), Tanturri (2–4), Mahler (5), de Bruijn(6) and Pennington (7). Euler and Tanturri were primarily concerned with deriving formulae for the precise calculation of b(n), whereas Mahler deduced an asymptotic formula for log b(n) from his analysis of the functions satisfying a certain class of functional equations. De Bruijn and Pennington extended Mahler's work and obtained more precise results.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 66 , Issue 2 , September 1969 , pp. 371 - 376
Copyright
Copyright © Cambridge Philosophical Society 1969

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References

REFERENCES

(1)Euler, L.Novi Comm. Petrop. III (1750).Google Scholar
(2)Tanturri, A.Atti Accad. Sci. Torino Cl. Sci. Fis. Mat. Natur. 52 (1916), 902–908.Google Scholar
(3)Tanturri, A.Atti Accad. Sci. Torino Cl. Sci. Fis. Mat. Natur. 54 (1918), 69–82.Google Scholar
(4)Tanturri, A.Atti. Accad. Naz. Lincei Mem. Cl. Sci. Fis. Mat. Natur. Sez I. 27 (1918), 399–403.Google Scholar
(5)Mahler, K.J. London Math. Soc. 15 (1940), 115–123.CrossRefGoogle Scholar
(6)De Bruijn, N. G.Nederl. Akad. Wetensch. Proc. Ser. A 51 (1948), 659–669.Google Scholar
(7)Pennington, W. B.Ann. of Math. 57 (1953), 531–546.CrossRefGoogle Scholar
(8)Dickson, L. E.History of the theory of numbers, vol. 2 (1952) (Chelsea Publishing Co., New York, 1952).Google Scholar