A sequence is such that its terms are generated by the formula: $$r_i =(ar_{i-1}+b\pmod m)$$
where $a,b,m,r_0$ are given.
find the period,that is the number of terms that are repeated.
For example, if $a = 2, b = 6, m = 12, r_0 = 11$, the generated sequence will be: $4, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10$, ...
period of this is 2 because 2,10 are repeating
how to find the period?