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Math Help - True or False?

  1. #1
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    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!
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  2. #2
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    Quote Originally Posted by GreenDay14 View Post
    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) q_1q_2 a^2=a(q_1q_2a)
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  3. #3
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    Thanks a lot focus !
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