Let A = {x e Z: (7x + 39) mod 17 = 14}. a) Find a number ß such that (7B) mod 17 = 1. b) Prove that there exists a number z e {0, 1, ..., 16) such that A = {x € Z:x mod 17 = z}. c) Find z. (Hint: Use modular arithmetic.)

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A: Given that x is an integer. To show :(a) gcd (x+1,x2-x+1) divides 3 (b) To determine for which…

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A: We use primitive roots to solve this problem.

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A: By the help of even and odd integer's we prove the result. The answer is given as follows :

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A: I hove used the theorem on congruent

Q: 61 Let A = Compute 612 - A and (612)A. 4 2

A: Step 1: Step 2: Step 3: Step 4:

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A: The solution is given as follows

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A:

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A: Consider the given expression.

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A: Details attached as step 2.

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A: