Let p be a large prime number, K, L, M, λ be integers with 1 ≤ M ≤ p and gcd(λ, p) = 1. The aim of our paper is to obtain sharp upper bound estimates for the number I 2(M; K, L) of solutions of the congruence $$xy \equiv \lambda \quad ({\rm mod} p), \quad K+ 1 \leq x \leq K +M,\quad L+ 1 \leq y \leq L +M,$$ and for the number I 3(M;L) of solutions of the congruence $$xyz \equiv \lambda \quad ({\rm mod} p), \quad L+ 1 \leq x, y, z \leq L +M .$$ Using the idea of Heath-Brown from [H], we obtain a bound for I 2(M; K, L), which improves several recent results of Chan and Shparlinski [CS]. For instance, we prove that if M < p 1/4, then I 2(M; K, L) ≤ M o(1). The problem with I 3(M; L) is more difficult and requires a different approach. Here, we connect this problem with the Pell diophantine equation and prove that for M < p 1/8 one has I 3(M;L) ≤ M o(1). Our results have applications to some other problems as well. For instance, it follows that if $${\mathcal{I}_{1},\,\mathcal{I}_{2},\,\mathcal{I}_{3}}$$ are intervals in $${{\mathbb{F}_{p}^{*}}}$$ of length $${{|\mathcal{I}_{1}| < p^{1/8}}}$$ , then $$|\mathcal{I}_{1}\,\cdot \,\mathcal{I}_{2}\,\cdot \mathcal{I}_{3}| = (|\mathcal{I}_{1}|\,\cdot\,|\mathcal{I}_{2}|\,\cdot\,|\mathcal{I}_{3}|)^{1-o(1)}$$ .