Lower and upper bounds for solutions of the congruence xm ≡ a(mod n)

Let n, m be natural numbers with n ≥ 2. We say that an integer a, (a, n) = 1, is the m-th power residue modulo n if there exists an integer x such that x^m ≡ a(mod n). Let C(n) denote the multiplicative group consisting of the residues modulo n which are relatively prime to n. Let s(n, m, a) be the smallest solution of the congruence x^m ≡ a(mod n) in the set C(n). Let t(n, m, a) be the largest solution of the congruence x^m ≡ a(mod n) in the set C(n). We will give an upper bound for s(n, m, a) and a lower bound for t(n, m, a).