Given $x_{n+1}=1229x_n \pmod{2048}$ and $u_n=x_n/2048$, I have to find the number of lines on which the points $(u_n,u_{n+1})$ lie.
I know that by Marsaglia's theorem, this will be $(2048\cdot 2)^{1/2}=64$. But is there a way of determining this without using this theorem? A more elementary way.