6 Euler's Totient Theorem Euler's Totient Theorem states that, if n and a are coprime, a?(") = 1 (mod n) where o (n) (known as Euler's Totient Function) is the number of positive integers less than or equal to n which are coprime to n (including 1).(a) Let the numbers less than n which are coprime to n be m1,m2, . . . ,m(n). Argue that the set {am1,am27 . . . ,am(n)} is a permutation of the set {m1,m2,. . . ,m(n)}. In other words, prove that f I {m1,m2,...,m(n)} > {m1,m2,...,m(n)} is a bijection, where f (x) := ax (mod n). (b) Prove Euler's Theorem. (Hint: Recall the FLT proof.)