Let n Z. Prove each of the statements (a)(f).(a) If n 0 (mod 7), then n2 0 (mod 7).(b)

Chapter 4, Problem 4.22

(choose chapter or problem)

Let n Z. Prove each of the statements (a)(f).(a) If n 0 (mod 7), then n2 0 (mod 7).(b) If n 1 (mod 7), then n2 1 (mod 7).(c) If n 2 (mod 7), then n2 4 (mod 7).(d) If n 3 (mod 7), then n2 2 (mod 7).(e) For each integer n, n2 (7 n)2 (mod 7).(f) For every integer n, n2 is congruent to exactly one of 0, 1, 2 or 4 modulo 7.

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