Modular arithmetic, even when disguised as a rounding problem, can be just as simple, if not simpler. The technique discussed here works for any constant N , delivers solutions even when x has 32 or ...

Ravi S. Kulkarni, An Arithmetic-Geometric Method in the Study of the Subgroups of the Modular Group, American Journal of Mathematics, Vol. 113, No. 6 (Dec., 1991), pp. 1053-1133 ...