In number theory, Euler`s totient or phi function, φ(n), is an arithmetic function that counts the totatives of n, that is, the positive integers less than or equal to n that are relatively prime to n. Thus, if n is a positive integer, then φ(n) is the number of integers k in the range 1 ≤ k ≤ n for which gcd(n, k) = 1. The totient function....