Question 135
Consider a sequence $x_{n}$ such that $x_{1}=x_{2}=1$, $x_{3} = \frac{2}{3}$. Suppose that $x_{n} = \frac{x_{n-1}^{2} x_{n-2}}{2 x_{n-2}^{2} - x_{n-1} x_{n-3}}$ for all $n \geq 4$. Find the least $n$ such that $x_{n} \leq \frac{1}{10^{6}}$.