Let $ x,~y~$ are two natural numbers such that $~x,~y \in (0,1001)~$ and also satisfying $~x^2=1+4y.$ Then how many ordered pair of such $~(x,y)~ $ are possible?
First notice that , $x$ is odd natural number, so there exists a positive integer $n$ such that $~x=2n+1.$ Then we have $~y=n^2+n.$
From here how can I find the possible pairs of $~(x,y)~$ such that $~x,y~$ are natural numbers and $x^2=1+4y.$
Please help me to solve this.