Find the Period of F(mod m)

Yes, here is exactly the web site you've been looking for! It is known that when the Fibonacci sequence is reduced to the sequence of residues under a modulus, that it becomes periodic. So, you naturally wonder "What is the period of F(mod m)???" Good question! Here you can enter a modulus, 1 < m < 10000000, and see what the period of F(mod m) is. Have fun!

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

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

Enter a modulus:
 Press:
 Result:
Period =
# Zeros =
m = 9999939
k = 13333256
time = about 7 minutes
This page created by Marc Renault