Question 440607
From this line:


[My “idea”: b = a·r, c = b·s, c = (a·r)·s = a·(r·s). Don't know the rest.] 


You've essentially proven the statement. a|c if and only if c = a*k, where k is some integer. Since c = a*(r*s), and r*s is an integer, then c is equal to a times some integer, a|c, QED.