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Math Help - Divisibilty proofs?

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    Divisibilty proofs?

    Mathematical signs
    Last edited by thegarden; December 2nd 2008 at 09:20 AM.
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  2. #2
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    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. a|1 \implies 1 = ab \implies a=\pm 1.

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