Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-26T01:08:04.730Z Has data issue: false hasContentIssue false
  • English
  • Français

Integer solutions of systems of quadratic equations

Published online by Cambridge University Press:  24 October 2008

J. L. Britton
J. L. Britton
Affiliation:
Queen Elizabeth College, London
Get access Rights & Permissions [Opens in a new window]

Extract

As is well known, there is an algorithm for deciding if a system of linear equations with coefficients from the set Z of integers has a solution in integers. The purpose of this paper is to answer the following question: does this remain true if ‘linear’ is replaced by ‘quadratic’?

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 86 , Issue 3 , November 1979 , pp. 385 - 389
Copyright
Copyright © Cambridge Philosophical Society 1979

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

(1)Cassels, J. W. S.Rational quadratic forms (London, Academic Press, 1978).Google Scholar
(2)Davis, M., Putnam, H. and Robinson, J.he decision problem for exponential diophantine equations. Ann. of Math. 74 (1961), 425–436.CrossRefGoogle Scholar
(3)Lloyd, D.Bounds for solutions of diophantine equations, Bull. Australian Math. Soc. 14 (1976), 467–469.CrossRefGoogle Scholar
(4)Matijasevic, Ju. V.Enumerable sets are diophantine. Soviet Math. Dokl. 11 (1970), no. 2, 354–8.Google Scholar
(5)Mordell, L. J.The minimum of an inhomogeneous quadratic polynomial in n variables. Math. Z. 63 (1956), 525–528.CrossRefGoogle Scholar
(6)Mordell, L. J.Integer solutions of simultaneous quadratic equations. Abh. Math. Sem. Hamburg 23 (1959), 126–143.CrossRefGoogle Scholar
(7)Siegel, C. L.Zur Theorie der quadratischen Formen. Nachr. Akad. Wiss. Gottingen Math. Phys. Kl. II (1972), 21–46.Google Scholar
(8) Swinnerton-Dyer, H. P. F.Rational zeros of two quadratic forms. Acta Arith. 9 (1964), 261–270.CrossRefGoogle Scholar