Hey guys, I need a bit of help here.

1. Show that the equation has no integer solution using Legendre symbol.

So

So because it equals , is a quadratic non-residue modulo and so there is no integer solution to .

Is this enough to show no integer solutions?

2. Evaluate the Legendre symbol for odd prime .

So

What is the formal way to go from here?

I have evaluated this for several cases of odd prime p and kind of see a pattern.

Also, this value alternates between -1 and 1 for odd numbers.

Any help guys?

Thanks for your help.