Problem 5 (Parts a and b) (a) Let x € Z. Prove that if 2 | (x2-5), then 4 | (x²-5). (b) Give an example of an integer x

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Problem 5 Parts A And B A Let X Z Prove That If 2 X2 5 Then 4 X 5 B Give An Example Of An Integer X 1 (23.19 KiB) Viewed 33 times

Problem 5 (Parts a and b) (a) Let x € Z. Prove that if 2 | (x2-5), then 4 | (x²-5). (b) Give an example of an integer x such that 2 | (x²-5) but 8 X(x²-5). Problem 6 Let n € Z. Prove that 2 | (n-3) if and only if 4 | (n² + 3). Problem 7 Let a, b, ne Z, where n ≥ 2. Prove that if a = b (mod n), then a² b² (mod n). Problem 8 Let a, b, c, n e Z, where n ≥ 2. Prove that if a b (mod n) and a = c (mod n), then b = c (mod n).