Problem 6 Let n € Z. Prove that 2 | (n-3) if and only if 4 | (n²+3). Problem 7 Let a, b, n € Z, where n ≥ 2. Prove that

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Problem 6 Let N Z Prove That 2 N 3 If And Only If 4 N 3 Problem 7 Let A B N Z Where N 2 Prove That 1 (20.69 KiB) Viewed 46 times

Problem 6 Let n € Z. Prove that 2 | (n-3) if and only if 4 | (n²+3). Problem 7 Let a, b, n € Z, where n ≥ 2. Prove that if a = b (mod n), then a² = b² (mod n). Problem 8 Let a, b, c, n € Z, where n ≥ 2. Prove that if a = b (mod n) and a = c (mod n), then b = c (mod n). Problem 9 Prove that if a is an integer such that a = 1 (mod 5), then a² = 1 (mod 5).