21 Jun
2005
21 Jun
'05
12:50 p.m.
I wrote: << Consider the Fibonacci sequence F_0 = 0, F_1 = 1, F_2 = 1, ... reduced mod n for fixed n >= 2. . . . Define fp(n) := the least period of {F_k mod n}. QUESTION: What is a formula for fp(n) in general?
Hmmm, one pattern that seems to hold is that for any prime p, fp(p^2) = p*fp(p). E.g., fp(1) = 1*1, fp(4) = 2*3, fp(9) = 3*8, fp(25) = 5*20, fp(49) = 7*16, fp(121) = 11*10, fp(169) = 13*28. I wonder why. --Dan