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Number Theory: Let p be an odd number. Recall that a primitive root, mod p, is an...

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Advance Math

Number Theory:

Let p be an odd number. Recall that a primitive root, mod p, isan integer g such that gp-1 = 1 mod p, and no smallerpower of g is congruent to 1 mod p. Some results in this chaptercan be proved via the existence of a primitive root(Theorem6.26)

(c) Given a primitive root g, and an integer a such that a isnot congruent to 0 mod p, prove that a is a square modulo p if andonly if a = ge for an even number e. Use this to proveEuler's criterion: a is a square mod p if and only ifa(p-1)/2 = 1 mod p.

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