FIBONACCI SEQUENCES OF PERIOD n IN GROUPS

A helpful starting point is the paper entitled "Fibonacci Series Modulo m by D. D. Wall [3]. With Wall, we let /„ denote the n member of the sequence of integers fQ = a, f1 = b9 ..., where fn + 1 = fn + f n _ r The symbol h(m) will denote the length of the period of the sequence resulting from reducing each /„ modulo w. The basic Fibonacci sequence will be given by uQ = 0, ux = 1, ... and the Lucas sequence by v0 = 2, v1 = 1, ... . The symbol k(m) will denote the lenght of the period of the basic Fibonacci sequence 0, 1, 2, 3, ... when it is reduced modulo m« Since we will often work in a group setting, we will let 7L and lLm represent the group of integers and the group of integers modulo m3 respectively. We summarize some of Wall's results in the following, using a group setting for convenience,