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(Solved): (6) Let a and k be as in (5). Prove that (i) a 2 1 mod 2 if, and only if, a 1 mod 2; (ii) a ...
(6) Let a and k be as in (5). Prove that (i) a 2 ? 1 mod 2 if, and only if, a ? 1 mod 2; (ii) a 2 ? 1 mod 22 if , and only if, a ? ±1 mod 22 ; (iii) For k ? 3 we have a 2 ? 1 mod 2k if, and only if, a ? ±1 mod 2k or a ? 2 k?1±1 mod 2k .