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Math Help - distinct pairs

  1. #1
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    distinct pairs

    find the number of disttinct pairs of postive integers (m,n)such that n(m-n)=2009
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  2. #2
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    Quote Originally Posted by banku12 View Post
    find the number of disttinct pairs of postive integers (m,n)such that n(m-n)=2009

    2009=7^2\cdot 41\Longrightarrow\,n must be taken from the divisors 1,\,7,\,49,\,41,\,287,\,2009 , and then you must choose m accordingly.

    For example, n=1\Longrightarrow\, m=2010\,:\,1(2010-1)=2009\;;\;\;n=7\Longrightarrow\,m=294\,: 7(294-7)=7\cdot 287=2009 , etc.

    Tonio
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