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Math Help - need help on this discrete problem

  1. #1
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    Feb 2008
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    need help on this discrete problem

    gcd(a,b)=1 if and only if gcd(a,a+b)=1

    prove.....
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  2. #2
    Senior Member
    Joined
    Dec 2007
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    Melbourne
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    suppose gcd (a,b) = k.
    k|a and k|b => k|(a+b)
    So \gcd (a,a+b) \geq k since k is a common divisor.
    So if \gcd (a,b) \not = 1 then \gcd (a,a+b) \not = 1
    Taking the contrapositive gives us gcd (a, a+b) = 1 => gcd (a,b) = 1

    suppose gcd (a, a+b) = p. Then the proof for this direction is very very similar to the previous direction.
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  3. #3
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    Feb 2008
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    alright that makes sense thanks a lot for the help.
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