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Math Help - relatively prime problem

  1. #1
    Junior Member
    Joined
    Feb 2009
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    relatively prime problem

    Hi,

    Need help with this problem;

    Let a,b1,b2,....bn E Z, with (a,b1)=(a,b2)=(a,b3)=....=(a,bn)=1

    Prove that

    (a,b1b2....bn) = 1

    Thanks
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  2. #2
    MHF Contributor
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    South Coast of England
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    Prime factors

    Hello htata123
    Quote Originally Posted by htata123 View Post
    Hi,

    Need help with this problem;

    Let a,b1,b2,....bn E Z, with (a,b1)=(a,b2)=(a,b3)=....=(a,bn)=1

    Prove that

    (a,b1b2....bn) = 1

    Thanks
    You need to consider the (unique) prime factorisation of a and all the b_i, and then use the fact that a does not have any prime factor in common with any of the b_i, and therefore neither with \prod{b_i}.

    Grandad
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