BdMO Online Forum

mac0220 wrote: ↑

Mon Mar 05, 2018 9:38 am

The solution is ( m,n ) = (2,2)
n and n-1 are co prime unless n-1=1
which makes n=m=2

samiul_samin wrote: ↑

Sun Feb 18, 2018 12:55 pm

Solution

$m+n=mn$
$\Rightarrow m+n=m+m+m+m+m+m+...+m $ (n times)
$\Rightarrow n=m+m+m+m+m....+m+m$ {(n-1)times}
$\Rightarrow n=m(n-1)\Rightarrow \dfrac {n}{n-1}=m$
But $n$ and $n-1$ are co-prime.
So, $m$ cannot be an integer.
A Contrudiction
So,there are no such $(m,n) $that satisfies the equation $m+n=mn$