$M>0$ is an integer.
For every $n>-0$ the remainder for the n Fibonacci number divided by m is: $r_n = f_n mod n$.
I need to prove that in :
$((r_n,r_n+1)) = (r_0,r_1),(r_1,r_2),(r_2,r_3)...$ must be repeats of pairs
Will appreciate some guidance because I don't know where to start...