Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-24T16:22:33.558Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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