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.

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- January 21st 2008, 12:53 PMtttcomraderCongruence 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. - January 21st 2008, 01:05 PMThePerfectHacker
Use Euler's criterion. Thus, is a quadradic residue if and only if hence if then is even and the congruence holds.