Prove that if and is prime then is a quadratic residue .

I believe I need to show that . Will someone show me where to start? I have been thinking about this problem all weekend.

Thanks in advance,

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- Jul 17th 2011, 08:45 AMZalrenproof with quadratic residue
Prove that if and is prime then is a quadratic residue .

I believe I need to show that . Will someone show me where to start? I have been thinking about this problem all weekend.

Thanks in advance, - Jul 17th 2011, 12:51 PMBruno J.Re: proof with quadratic residue
Well, if , that doesn't leave you much choice for the value of , does it?

- Jul 17th 2011, 02:03 PMZalrenRe: proof with quadratic residue
Oops, I typed it wrong. I corrected it!

- Jul 17th 2011, 02:20 PMZalrenRe: proof with quadratic residue
What if I started like this:

Using Quadratic Reciprocity Theorem: since is an even exponent. That tells me that

, I believe this is a true statement, how do I back it up?

So - Jul 17th 2011, 03:22 PMBruno J.Re: proof with quadratic residue
.

And is not even if ... - Jul 17th 2011, 04:17 PMZalrenRe: proof with quadratic residue
So can I assume , for example , and just show the specific case where and show that ?