Let G (a) be a cyclic group of order n. For each integer m, define a map fm : G -> G by fm(x) т = x"" for every x E G. Prove that (1) fm is a group homomorphism. (2) fm is an automorphism if and only...

Extracted text: Let G (a) be a cyclic group of order n. For each integer m, define a map fm : G -> G by fm(x) т = x"" for every x E G. Prove that (1) fm is a group homomorphism. (2) fm is an automorphism if and only if gcd(m, n) = 1. (3) Find the kernel and image of f4 whenn = т т 10.