Divisors in residue classes, constructively

Let r, s, n be integers satisfying 0 <= r < s < n, s >= n(alpha), alpha > 1/4, and let gcd(r, s) = 1. Lenstra showed that the number of integer divisors of n equivalent to r (mod s) is upper bounded by O((alpha - 1/4)(-2)). We re-examine this problem, showing how to explicitly construct all such divisors, and incidentally improve this bound to O((alpha - 1/4)(-3/2)).