Research Article

Small solutions of quadratic congruences, II

D. R. Heath-Browna1

a1 Magdalen College, Oxford, OX1 4AU

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


(Received January 23 1991)

Key Words:

  • 11D79: NUMBER THEORY; Diophantine equations; Congruences in many variables.