Evaluate the proposed proof of the following result.Result Let x, y Z. If x 1 (mod 3)
Chapter 4, Problem 4.87(choose chapter or problem)
Evaluate the proposed proof of the following result.Result Let x, y Z. If x 1 (mod 3) and y 1 (mod 3), then x y 1 (mod 3).Proof Assume that x 1 (mod 3) and y 1 (mod 3). Then 3 | (x 1) and 3 | (y 1). Hencex 1 = 3q and y 1 = 3q for some integer q and so x = 3q + 1 and y = 3q + 1. Thusx y = (3q + 1)(3q + 1) = 9q2 + 6q + 1 = 3(3q2 + 2q) + 1and so x y 1 = 3(3q2 + 2q). Since 3q2 + 2q is an integer, 3 | (x y 1). Hence x y 1 (mod 3).
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