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Help with a proof

  1. Jan 27, 2008 #1
    Hi there can someone help me on this one:
    If gcd(a,b)=1 then gcd(a,bk) = gcd(a,k)

    I have arrived at the conclusion that gcd(a,bk) gcd(a,k) both divide k but from here I do not get anywhere.

    I would like some hints on this please.
     
  2. jcsd
  3. Jan 28, 2008 #2
    Hi, I think it is sufficient to prove that gcd(a,bk) and gcd(a,b) divide each other.
     
  4. Jan 28, 2008 #3
    could be that they both equal 1, for instance if k = b but think of expressing both a and k in the form of a product of primes. Since the gcd(a,k) is the product of the prime factors that are common to a and k or 1 if there are no common factors other than 1, and gcd(a,b), which is the product of the prime factors that are common to b and a, is 1, does k*b add any other factors of a?
     
    Last edited: Jan 28, 2008
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