Pisano Periods (找规律)

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一、问题：

Description

In 1960, Donald Wall of IBM, in White Plains, NY, proved that the series obtained by taking each element of the Fibonacci series modulo m was periodic. For example, the first ten elements of the Fibonacci sequence, as well as their remainders modulo 11, are:

                   n |  1    2     3     4     5     6     7     8     9    10

             F (n) |  1    1     2     3     5     8    13   21   34   55

F (n) mod 11 |  1    1     2     3     5     8     2    10    1     0

The sequence made up of the remainders then repeats. Let k(m) be the length of the repeating subsequenc