### Compute the Period, Rank, and Order of F(mod m)

Enter a modulus, 1 < m < 100,000,000 and compute the period, rank, order, and multiplier of F(mod m).

The **period** of F(mod m) is the number of terms before the sequence repeats.

The **rank** of F(mod m) is the least positive integer r such that F_{r} = 0 (mod m).

The **order** of F(mod m) is period/rank. Note that the zeros of F(mod m) are evenly spaced.

If F(mod m) has rank r, then the **multiplier** of F(mod m) is F_{r+1} (mod m).

For more information see my article The Fibonacci Sequence
Modulo M.

Or, see a list of the first 2000 moduli and periods.

This page created by Marc Renault