Suppose and . If and are relatively prime, prove that has order .
So suppose and . Then . Thus or . So . Thus the order of is .
Is this correct?
NOTE: I am actually not sure if this is correct. Let another member validate this. I feel as though I may have made a stupid incorrect assumption.
Problem: Let . Prove that if that .
Proof: Clearly . Now suppose that then and . Thus . Similarly . And since we see that and since this is only true if . Similarly and since this means and by previous reasoning . Therefore which means that but since we have that and which is a contradiction since .