Anintegeristing problem .

Theorem:Let p be an odd prime the number of quadradic residues (modulo classes) is the same as the number of quadradic non-residues.

Proof:I can write the prove, but I am sure you learned this theorem.

Consider our incongruents integers:

1,2,...,p-1

The idea is that since the number of quadradic residues is equal to non-residues they MUST be next to each otherunlessthey alternate:

residue, non-residue, ...

(Sine 1 is residue).

But that cannot happen.

See if you can finish it.