Given the values of n below, determine, without exhaustive search, etc., how many integers k there are, with gcd(k, n) = 1, and 1 <= k <= n, such that k has a square root modulo n. Do this for (a) n = 143, (b) n = 286, (c) n = 572, (d) n = 1144, and (e) n = 2288. In each case, determine also phi(n), so as to be able to tell what fraction of reduced residue classes modulo n have square roots.
Given the values of n below, determine, without exhaustive search, etc., how many integers k ther...