Thanks for the help last time, I have 2 questions that I know are easy but I am hitting a block with all of my exams going on right now anyway..

1. Show that if a,n are positive integers and gcd(a,n)=1, then there exists a positive integer k, such that n divides((a^k)-1).

This one I should know but I can't seem to come up with the right procedure....

2. If m divides n, then m^2 divides n^2.

Thank you in advance.