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GCD = 1 Proof

  1. Aug 31, 2011 #1
    1. The problem statement, all variables and given/known data
    If gcd(ab,c) = 1 then gcd(a,c)=1 and gcd(b,c)=1


    2. The attempt at a solution
    Well, if gcd(ab,c) = 1 we know that

    abk + cl = 1 for some integers k and l

    not really sure where to go from here... any hints?
     
  2. jcsd
  3. Sep 1, 2011 #2

    Char. Limit

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    Gold Member

    Also, if gcd(a,c)=1, then am+cn=1 for some integers m and n. Now what if m=bk?

    Repeat for the other one.
     
  4. Sep 1, 2011 #3
    oh wow, that is painfully obvious .... thanks Char. Limit !
     
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