Hey, I have a question here asking to figure out whether the following are true or false and then provide either a proof or counter-example.
i) If a|b, and c|b, then ac|b
For this I made the attempt: if a|b then b=ax for any integer x, and if c|b then b = cx for any integer x. So b = a(c/b), but I don't know if I am in the right direction here or if I am completely wrong?
ii) If a|b and a|c, then a|bc.
For this I said: if a|b then b=q1a and if a|c then c=q2a. So bc = q1a*q2a.... and then I am lost...
Did I make any sense in either of these? Could someone please point me in the right direction. Thanks!