Abstract
Let Q(x) = Q(x(1), x(2),..., x(n)) be a quadratic form over Z and p be an odd prime. Let V = V-Q = V-p(2) denote the set of zeros of Q(x) in Z(P)(2) and vertical bar V vertical bar denote the cardinality of V. Set phi(V-p(2),y) = Sigma(x is an element of v) e (2)(p) (x . y) for y # 0 and phi(V-p(2), y) vertical bar Vp vertical bar -p(2(n-1)) for y = 0. In this paper, we are interested to determine the number of integer solutions of the congruence Q(x) = 0 (mod p(2)).