(a) For a prime p, show that if p is a prime that can be written...

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(a) For a prime p, show that if p is a prime that can be written as a sum of two perfect squares, so p = a² +b with alp and b1 p, then-1 must be a perfect square mod p. (a) For a prime p, show that if p is a prime that can be written as a sum of two perfect squares, so p = a² +b with alp and b1 p, then-1 must be a perfect square mod p.