(a) Let r be a primitive root of the odd prime p. Establish that the exponential

Chapter 8, Problem 16

(choose chapter or problem)

(a) Let r be a primitive root of the odd prime p. Establish that the exponential congruenceax =b(mod p)has a solution if and only if d I indr b, where the integer d = gcd(indr a, p - 1); inthis case, there are d incongruent solutions modulo p - 1.(b) Solve the exponential congruences 4x = 13 (mod 17) and 5x = 4 (mod 19).

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