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Small solutions of quadratic and quartic congruences

Published online by Cambridge University Press:  26 February 2010

R. C. Baker
R. C. Baker
Affiliation:
Royal Holloway College, Egham, Surrey
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Extract

The present investigation was suggested by a theorem of A. Schinzel, H. P. Schlickewei and W. M. Schmidt [6]: let Q(x) = Q(x1,…, xs) be a quadratic form with integer coefficients. Then for each natural number m there are integers x1,…, xs satisfying

and having

Type
Research Article
Information
Mathematika , Volume 27 , Issue 1 , June 1980 , pp. 30 - 45
Copyright
Copyright © University College London 1980

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References

1.Baker, R. C. and Schmidt, W. M.. “Diophantine problems with variables restricted to 0 and 1”, J. Number Theory (to appear).Google Scholar
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6.Schinzel, A., Schlickewei, H. P. and Schmidt, W. M.. “Small solutions of quadratic congruences and small fractional parts of quadratic forms”, Acta Arith. (to appear).Google Scholar
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8.Schmidt, W. M.. “Diophantine inequalities for forms of odd degree”, Advances in Math, (to appear).Google Scholar