1.Let G be a group. Let H and K be subgroups of G such that #H = 39 and #K = 65. Prove that H K is cyclic. Hint: You needn't prove that H K is a group. Just prove that it is cyclic.

2.Let m,n be positive integers with (m,n) = 1. Prove that there is no homomorphism from Zm to Zn other than the constant one.