[math-fun] period of fibonacci sequence mod n

Obviously, the greatest period we could hope for would be (n*n-1). This is achieved when n=2 and n=3, but for no other n up to 270000. If we merely ask that period>=(n*n-1)/2, or period>=n^(3/2), that happens for n=2,3,5,6,10, but for no other n up to 270000. If we merely ask that period>=5*n, that happens for n=10,50,250,1250,6250,31250, and which all are of form 2*5^k, but for no other n up to 270000. Note in particular that n=156250=2*5^7 is NOT listed. In all six of these cases, the period equals 6*n. Periods exceeding n seem to happen about 10% of the time. No case where period>10*n happens up to 270000. -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)