1.
So, 19 is a quadratic non-residue modulo 71 and therefore the equation has no integer solutions.
2.
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.