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On the representations of a number as a sum of squares and certain related identities

Published online by Cambridge University Press:  24 October 2008

R. A. Rankin
R. A. Rankin
Affiliation:
Clare CollegeCambridge
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Extract

Let Rc(n) be the number of representations of any non-negative integer n as the sum of c squares; i.e. Rc(n) is the number of different solutions (x1, x2, …, xc) of the equation

where the xμ are integers, and may be positive, negative, or zero. Two such solutions, (x1, x2, …, xc) and are only considered to be the same solution if

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 41 , Issue 1 , June 1945 , pp. 1 - 11
Copyright
Copyright © Cambridge Philosophical Society 1945

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References

REFERENCES

1Bachmann, P.Niedere Zahlentheorie (Leipzig, 1901–1910).Google Scholar
2Glaisher, J. W. L.On the representations of a number as a sum of four squares, and on some allied arithmetical functions. Quart. J. Math. 36 (1905), 305–58.Google Scholar
3Glaisher, J. W. L.On elliptic-function expansions in which the coefficients are powers of the complex numbers having n as norm. Quart. J. Math. 39 (1908), 266–300.Google Scholar
4Liouville, M. J.Note sur une question de théorie des nombres. Journal de Math. (2), 3 (1858), 357–60.Google Scholar
5Stern, M.Beweis eines Liouvilleschen Satzes. J. reine angew. Math. 105 (1889), 250–66.CrossRefGoogle Scholar
6Tannery, J. and Molk, J.Fonctions elliptiques (Paris, 1893–1902).Google Scholar
7Vahlen, K.Th. Beiträge zu einer additiven Zahlentheorie. J. reine angew. Math. 112 (1893), 1–36.Google Scholar
8Van der Waerden, B. L.Moderne Algebra (Berlin, 1937);CrossRefGoogle Scholar
Van der Waerden, B. L.Moderne Algebra (New York, 1943).Google Scholar