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

Number Theory:

Let p be an odd number. Recall that a primitive root, mod p, is an integer g such that g^p-1 = 1 mod p, and no smaller power of g is congruent to 1 mod p. Some results in this chapter can be proved via the existence of a primitive root(Theorem 6.26)

(c) Given a primitive root g, and an integer a such that a is not congruent to 0 mod p, prove that a is a square modulo p if and only if a = g^e for an even number e. Use this to prove Euler's criterion: a is a square mod p if and only if a^(p-1)/2 = 1 mod p.

Expert Solution

Colby Messinger answered 3 years ago

Let p be an odd prime. (a) (*) Prove that there is a primitive root modulo...

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Number Theory Show that 18! = -1 (mod 437 = 19x23)

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