Find all ordered pair of integers $(x,y)$ 
Obtain all ordered pair of integers $(x,y)$ such that $$x(x + 1) = y(y + 1)(y + 2)(y + 3)$$

I'm getting 8, 
(0, 0), (0, -1), (0, -2), (0, -3)
(-1, 0), (-1, -1), (-1, -2), (-1, -3)
Please confirm my answer.

Hint: It is easily proved that the product of four consecutive integers, plus $1$, is a perfect square. But $x(x+1)+1$ is hardly ever a perfect square!
Added: To prove that $y(y+1)(y+2)(y+3)+1$ is a perfect square, note that 
$$y(y+1)(y+2)(y+3)=y(y+3)(y+1)(y+2)=(y^2+3y)(y^2+3y+2)=z(z+2),$$
where $z=y^2+3y$. And clearly $z(z+2)+1=(z+1)^2$. 
