.Hi, I just registered for this site, and it looks like a pretty neat place.
I just needed a confirmation that I did a couple proofs right. I'm taking Number Theory at my university, and on Tuesday I have to teach the class two proofs.
My first one is to prove that has exactly two solutions: 1 and p-1
proof: let be any solution. SO we have so thus
Because p is a prime (this is important) . Correct.
otherwise expressed as . So . Since r is a least residue (modp) we have r = p -1 or 1
Correct. Note that ...
The other one I have to do is prove that if (a,m) doesnt divide b, then has no solutions.
Proof: We can prove this by looking at the contrapositive, which is logically equivalent. So if then has a solution.
This is not the contrapositive! It is "if has a solution then .
Let r be a solution, so . Thus, and there exists an integer k such that . Since and it follows that
Thanks guys I appreciate it