hello, rewrite it in the form $(x-1)^2-2007y^2=1$ and you will get a Pell equation. Sonnhard.

Dr Sonnhard Graubner wrote: hello, rewrite it in the form $(x-1)^2-2007y^2=1$ and you will get a Pell equation. Sonnhard. yes it is pell equation $(x-1)^2-223(3y)^2=1$ but i dont think it is the way to solve it minimal solution is $(x,y)=(225,5)$

We can write $x(x - 2) = 3^2 \cdot 223 \cdot y^2$, from which it follows that either $x$ is divisible by $223$ or $x - 2$ is divisible by $223$. Taking $x =223$ gives $x - 2 = 221$ which is not a perfect square. Taking $x - 2 = 223$, or $x = 225$ works; the corresponding value of $y$ is $5$.