## BdMO National Higher Secondary 2015#2

samiul_samin
Posts: 1007
Joined: Sat Dec 09, 2017 1:32 pm

### BdMO National Higher Secondary 2015#2

Let $N$ be the number if pairs of integers $(m,n)$ that satisfies the equation $m^2+n^2=m^3$
Is $N$ finite or infinite?If $N$ is finite,what is its value?

samiul_samin
Posts: 1007
Joined: Sat Dec 09, 2017 1:32 pm

### Re: BdMO National Higher Secondary 2015#2

$m^2+n^2=m^3 \rightarrow n^2=m^2(m-1)$
If $K$ is positive integer then plugging the value $m=K^2+1$ gives infinite solution for this equation .
So,$N$ is infinte.