Abstract
Let Q(x) be a quadratic form over Z in n variables, p he an odd prime and parallel to x parallel to = max(i) vertical bar x(i)vertical bar solution of the congruence Q(x) equivalent to 0 (mod p(2)) is said to be nontrivial if p (sic) x(i) for some i. We prove that if this congruence has a nontrivial solution, then it has a nontrivial solution with parallel to x parallel to <= p. We also give estimates on the number of small nontrivial solutions of the congruence and show that there exists a set of n linearly independent nontrivial solutions of size parallel to x parallel to <= (2(n+1) +1)p, provided that n >= 4 is even and Q(x) is nonsingular (mod p).