Small zeros of quadratic forms mod $P^{2}$

Abstract

Let Q(x )= Q(x1 ,x 2, ..., xn) be a quadratic form over Z, p be an odd prime, and Δ = � (−1) n/2 det AQ/p � . A solution of the congruence Q(x) ≡ 0 (modp m ) is said to be a primitive solution if pxi for some i .W e prove that if this congruence has a primitive solution then it has a primitive