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Small solutions of quadratic congruences, II

Part of: Diophantine equations

Published online by Cambridge University Press:  26 February 2010

D. R. Heath-Brown
D. R. Heath-Brown
Affiliation:
Magdalen College, Oxford, OX1 4AU
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Let Q(x) = Q(x1,…, xn) є ęZ x1, …, xn] be a quadratic form. The primary purpose of this paper is to bound the smallest non-zero solution of the congruence Q(x) = 0 (mod q). The problem may be formulated as follows. We ask for the least bound Bn(q) such that, for any Ki > 0 satisfying

and any Q, the congruence has a non-zero solution satisfying

MSC classification

Secondary: 11D79: Congruences in many variables
Type
Research Article
Information
Mathematika , Volume 38 , Issue 2 , December 1991 , pp. 264 - 284
Copyright
Copyright © University College London 1991

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