1. (a, m)=(b, m)=1⇒(ab, m)=1 2. c∣ab and (c, a)=1⇒c∣b 3. If c is a common multiple of a and b then [a, b]∣c 4. [ma, mb]=m[a, b] for all int m>0 5. [a, b](a, b)=∣ab∣ 6. Let g>0, s be integers. Show that g∣s iff ∃ integers x, y such that s=x+y and (x, y)=g


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Question Number 124944 by udaythool last updated on 07/Dec/20

$1 . (a, m) = (b, m) = 1 \Rightarrow (a b, m) = 1$ $2 . c ∣ a b and (c, a) = 1 \Rightarrow c ∣ b$ $3 . If c is a common multiple of$ $a and b then [a, b] ∣ c$ $4 . [m a, m b] = m [a, b] for all int m > 0$ $5 . [a, b] (a, b) =∣ a b ∣$ $6 . Let g > 0, s be integers . Show$ $that g ∣ s iff \exists integers x, y such$ $that s = x + y and (x, y) = g$
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