* Find all positive integer solutions $x, y$ of the equation $y^{2}-x(x+1)(x+2)(x+3)=1$.
Let $x$ be any positive integer, it is easy to know the identity $x(x+1)(x+2)(x+3)+1=\left(x^{2}+3 x+1\right)^{2}$. According to the original equation, let $y=x^{2}+3 x+1$. Therefore, all positive integer solutions of the original equation are: $x$ takes any positive integer, $y=x^{2}+3 x+1$.