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Abstract Algebra

  1. Sep 21, 2010 #1

    silvermane

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    1. The problem statement:
    Consider 3 positive integers, a, b, c. Let [tex]d_{1}[/tex] = gcd(b,c) = 1. Prove that the greatest number dividing all three of a, b, c is gcd([tex]d_{1}[/tex],c)


    3. My go at the proof and thoughts:

    Well, I know that the common divisors of a and b are precisely the divisors of [tex]d_{1}[/tex]

    I also know that to get the gcd(a,b,c) we need to consider a,b's gcd with c to get the overall gcd for all three numbers.

    I think that I need to write it as a linear combination for a,b, and c, but I'm stuck. This problem seems easy too, but I think there's something that I'm missing. :frown:
     
  2. jcsd
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