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GCD of four Different Pairs

  1. May 13, 2014 #1
    1. The problem statement, all variables and given/known data
    Give an example of a set S of four (distinct) positive integers such that the greatest common divisor of all
    six pairs of elements of S is 6.

    2. Relevant equations



    3. The attempt at a solution

    Can I say that my numbers are in the form?
    6
    12
    18
    30
    Is this ok?
     
    Last edited: May 13, 2014
  2. jcsd
  3. May 13, 2014 #2

    NascentOxygen

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    Staff: Mentor

    Are you sure you have the question worded correctly? The title says four pairs, the question refers to six.
     
  4. May 13, 2014 #3

    Mentallic

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    Homework Helper

    You don't need to skip 24. Using 6 as your first number will guarantee that the gcd is 6 as long as all of your other integers are of the form 6n where n is an integer.
     
  5. May 13, 2014 #4
    Nascent,
    4 choose 2 at a time is 6 possible pairs of gcd.

    Mentallic,
    If I used gcd(12, 24) = 12 and it doesn't satisfy the conditions.
     
  6. May 13, 2014 #5

    Mentallic

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    Homework Helper

    Ahh that makes a lot more sense now. Then yes, what you've done is correct. It just needs to be of the form

    [tex]6p_1, 6p_2, 6p_3, 6p_4[/tex]

    where pn is a distinct prime or 1.
     
  7. May 13, 2014 #6
    Thanks :>
     
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