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A simple proof of Jacobi's four-square theorem

Published online by Cambridge University Press:  09 April 2009

M. D. Hirschhorn
M. D. Hirschhorn
Affiliation:
Department of Mathematics, University of New South Wales, Kensington, N.S.W., Australia, 2033
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Abstract

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A celebrated result, due to Jacobi, says that the number of representations of the positive integer n as a sum of four squares is equal to eight times the sum of the divisors of n which are not divisible by 4. We give a new and simple proof of this result which depends only on Jacobi's triple product identity.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 32 , Issue 1 , January 1982 , pp. 61 - 67
Copyright
Copyright © Australian Mathematical Society 1982

References

Hardy, G. H. and Wright, E. M. (1960), An Introduction to the Theory of Numbers (Fourth Edition, ClarendonPress).Google Scholar
Hirschhorn, M. D. (1976), ‘Simple proofs of identities of MacMahon and Jacobi’ Discrete Math. 16, 161–162.Google Scholar