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Math Help - Infinite series of positive integers - proving existence

  1. #1
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    Infinite series of positive integers - proving existence

    Prove that a series exist with the following propeties:
    - the series is infinite and contains of positive integers
    - no elements divide any of the others in the series
    - any two numbers have a >1 common divisor in the series
    - but there are no >1 numbers that divides all the elements of the sereis (so the greatest common divisor of the elements is 1)

    Thank you in advance!
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  2. #2
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    Sequence or series?

    In any case, here's an example of a set whose elements (I think) satisfy the given conditions:

    The set is generated by prime multiples of 6, 10, and 15. (i.e {6p | p is prime} U {10p | p is prime} U {15p | p is prime})

    So it exists! (if I'm correct hehehe)
    Last edited by Bingk; November 17th 2010 at 03:15 PM. Reason: Added text
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  3. #3
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    Thank you very much. I should'we written sequence, sorry, I always mix them up.
    Thanks!
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