Let p≥ 5 be a prime. Let g be a primitive root of p. (i). If g-¹ mod p is the modular inverse of g, prove that g-¹ is also a primitiv root of p. (ii). Prove that g‡ g-¹ (mod p). (Hint: Prove first that g = g-¹ (mod p) implies that g² = 1 (mod p).) iii). Recall that there are ((p)) (p-1) primitive roots of p among {1,2,...,p}. We denote them by 9₁, 92, ..., 96(p-1). Prove that =

Q: Show that log, q is irrational for any distinct prime numbers p and q. (Distinct here p# q.) means

A: To Determine :-  logp q is irrational for any distinct prime numbers p and q.

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A:

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Q: > 2 is a prime, then (12) Prove that if p and (1 2... p-1 p) generate Sp.

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A: Given:Given that k is apositive integer.To find:The kth root of 6 is Irrational.

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