Hey, I am having a difficult time trying to prove a few statements relating to Euler's Theorem.

1. Prove for any n: If are in , then is also in , using a contrapositive argument.

2. Prove: Every has an inverse modulo n in , by considering the linear congruence

3. Prove: For every the function defined by is a permutation.

I really don't know what to do for these.

Any help would be greatly appreciated.

Thanks