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Math Help - gcd

  1. #1
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    gcd

    (a,b)=1 and c divides a+b prove (a,c)=1 and (b,c)=1
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  2. #2
    o_O
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    Let d_{1} = (a,c) \geq 1 and d_{2} = (b,c) \geq 1.

    Since c \mid (a+b), then that means d_{1} \mid (a+b) and d_{2} \mid (a+b) as both d_{1}, d_{2} are factors of c.

    However, since d_{1} \mid (a+b) and d_{1} \mid a & d_{2} \mid (a+b) and d_{2} \mid b, then d_{1} \mid b and d_{2} \mid a.

    This means d_{1} \mid (a,b) and d_{2} \mid (a,b). But (a,b) = 1. Conclude?

    Can you conclude?
    Last edited by o_O; October 5th 2008 at 07:57 PM.
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