MathNet 1998 — Part 01 Question 54

$k$ is the positive root of the equation $x^{2} - 1998x - 1 = 0$. Define the sequence $x_{0}, x_{1}, x_{2}, \ldots$ by $x_{0} = 1$, $x_{n+1} = \left[ k x_{n} \right]$. Find the remainder when $x_{1998}$ is divided by $1998$.