Let c, d e Zand m E N. For each statement decide whether it is necessarily true, or whether it can be false. Justify your answer with a proof or provide a counterexample. (i) If c +d = 0 (mod m), then...

Let c, d e Zand m E N. For each statement decide whether it is necessarily true, or whether it can be false.<br>Justify your answer with a proof or provide a counterexample.<br>(i) If c +d = 0 (mod m), then gcd(c, m) = gcd(d, m).<br>(ii) If gcd(c, m) = gcd(d, m), then c+ d = 0 (mod m).<br>

Extracted text: Let c, d e Zand m E N. For each statement decide whether it is necessarily true, or whether it can be false. Justify your answer with a proof or provide a counterexample. (i) If c +d = 0 (mod m), then gcd(c, m) = gcd(d, m). (ii) If gcd(c, m) = gcd(d, m), then c+ d = 0 (mod m).

Jun 04, 2022

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Let c, d e Zand m E N. For each statement decide whether it is necessarily true, or whether it can be false. Justify your answer with a proof or provide a counterexample. (i) If c +d = 0 (mod m), then...

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