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Thread: division proof help

  1. #1
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    division proof help

    1. a,b and c are integers such that a|b and b|c. Prove that a^2 |(b^2 +bc).






    if a|b than

    $\displaystyle b = ma $ for some m in the integers

    if b|c

    $\displaystyle c = nb $ for some n in the integers,

    I know I need to show that if $\displaystyle a^{2} | (b^{2} + bc) $

    than

    $\displaystyle b^{2} + bc = k a^{2} $ for some k in integers.

    $\displaystyle b^{2} + bc = m^{2}a^{2} + ma nb $

    really stuck from here, not such if my working is correct so far either,


    any help appreciated.
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  2. #2
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    Re: division proof help

    Try substituting $\displaystyle ma$ for b in your last equation on the right side
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