Thread: Congruence in Z

Let p be prime in Z with Show that there is an integer with

Proof. Now I have p - 1 = 4k for some integers k. Then p = 4k - 1, pk = 4k^2 - k, so I have a square of something but with an extra k behind, how can I continue?

Thank you.

Originally Posted by tttcomrader

Let p be prime in Z with Show that there is an integer with

Use Euler's criterion. Thus, is a quadradic residue if and only if hence if then is even and the congruence holds.