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Thread: Divisibilty proofs?

  1. #1
    Oct 2008

    Divisibilty proofs?

    Mathematical signs
    Last edited by thegarden; Dec 2nd 2008 at 08:20 AM.
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  2. #2
    Global Moderator

    Nov 2005
    New York City
    Quote Originally Posted by thegarden View Post
    Proofs required for the following divisibility rules:

    1. a|1 implies a= plus or minus 1
    2. a|b and b|a IF AND ONLY IF (IFF) a= plus or minus b
    3. a|b IFF -a|b IFF a|(-b) IFF (-a)(-b)
    4. Let b>0. If a|b implies a is less than or equal to b
    Sorry for not inserting mathematical signs, new to the forum so just finding my way around, many thanks.
    Use definition of division. I do the first one. $\displaystyle a|1 \implies 1 = ab \implies a=\pm 1$.

    And second one $\displaystyle a|b \implies a = bc$, $\displaystyle b|a\implies b = ad$.
    Thus, $\displaystyle a = bc = adb \implies 1 = bd \implies d = \pm 1$ (assuming $\displaystyle a\not = 0$).
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