1. ## True or False?

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!

2. Originally Posted by GreenDay14
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!
i) what happens if you set a=b=c (say 2)?
ii)$\displaystyle q_1q_2 a^2=a(q_1q_2a)$

3. Thanks a lot focus !