Question: An integer a is called a quadraticresidue modulo p if a 0 ( m o d p ) and there is an integer b such

An integer a is called a quadraticresidue modulo p if a0(modp) and there is an integer b such that b2=a(modp). Let p3(mod4) be an odd prime.

i. Suppose that a is a quadratic residue modulo p. Prove that the only two roots of x2a in Z/pZ are a(p+1)/4.

ii. Show that (still under assumption p3(mod4)) -1 is not a quadratic residue modulo p.

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