# Math Help - distinct pairs

1. ## distinct pairs

find the number of disttinct pairs of postive integers (m,n)such that $n(m-n)=2009$

2. Originally Posted by banku12
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