Question 155
Given an integer $n \ge 2$, define $M_0(x_0, y_0)$ to be an intersection point of the parabola $y^2 = nx - 1$ and the line $y = x$. Prove that for any positive integer $m$, there exists an integer $k \ge 2$ such that $(x_0^m, y_0^m)$ is an intersection point of $y^2 = kx - 1$ and $y = x$.