Find the Pisano Period
GolfScript (28 25 24 23 chars)

~1.{(2$+}{.@+2$%}/+\-,)


Takes input in stdin, leaves it on stdout (or the stack, if you want to further process it...)

This correctly handles the corner cases (Demo).

As a point of interest to GolfScript programmers, I think this is the first program I've written with an unfold which actually came out shorter than the other approaches I tried.