a1 Department of Mathematics, Kansas State University, Cardwell Hall, Manhattan, Kansas 66506-2602, U.S.A.
Let Q(x) = Q(x1, x2,…, xn) be a quadratic form with integer coefficients. Schinzel, Schickewei and Schmidt [9, Theorem 1] have shown that for any modulus m there exists a nonzero such that
and ║x║≤m(1/2)+(1/2(n-1)), where ║x║ = max |xi|. When m is a prime Heath-Brown  has obtained a nonzero solution of (1) with ║x║≤m1/2 log m. Yuan  has extended Heath-Brown's work to all finite fields. We have proved related results in  and . In this paper we extend Heath-Brown's work to moduli which are a product of two primes. Throughout the paper we shall assume that n is even and n>2. For any odd prime p let
where det Q is the determinant of the integer matrix representing Q and is the Legendre symbol.
(Received December 12 1989)