Evaluate the proposed proof of the following result.Result Let x, y Z. If x 2 (mod 3)

Chapter 4, Problem 4.82

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Evaluate the proposed proof of the following result.Result Let x, y Z. If x 2 (mod 3) and y 2 (mod 3), then x y 1 (mod 3).Proof Let x 2 (mod 3) and y 2 (mod 3). Then x = 3k + 2 and y = 3k + 2 for some integer k. Hencex y = (3k + 2)(3k + 2) = 9k2 + 12k + 4 = 9k2 + 12k + 3 + 1= 3(3k2 + 4k + 1) + 1.Since 3k2 + 4k + 1 is an integer, x y 1 (mod 3).

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