Let q be an odd positive integer and let a be an integer coprime to q. For each integer b coprime to q with 1<b<q, there is a unique integer e coprimc to q with 1≤e≤q such that be≡a (rood q). Let N (a, q) denote the number of solutions of the congruence equation bc≡a (rood q) wlth 1≤b, c<q such that b,c are of opposite parity. The main purpose of this paper is using the properties of Dcdekind sums, the properties of Cochranc sums and the mean value theorem of Diriehlet L-thnetions to study the asymptotic property of the mean square value Σ(N(a,q)-2-1(q)2, and give a sharp asymptotic formula.