@inbook {MATHEDUC.05602466,
author = {Rehlich, Hartmut},
title = {The length of cycles in Fibonacci-sequences modulo $M$.},
year = {2008},
booktitle = {Problem solving in mathematics education. Proceedings of the 9th ProMath conference, L\"uneburg, Germany, August 30-- September 2, 2007},
isbn = {978-3-88120-473-6},
pages = {153-168},
publisher = {Hildesheim: Franzbecker},
abstract = {Summary: A simple logical conclusion, using Dirichlet's box principle, proves that the Fibonacci-sequence module $M$ is cyclic for every $M$. But how long are the cycles? Material collected for the purpose of pattern-identification rapidly leads to different hypotheses. For some, we will outline proofs; others are intended as challenges for further work in incentive groups and seminars. The same applies to the second problem area in which a cyclic fill-in process (model of Phyllotaxis) is examined. In this process, $n$ regularly arranged positions on the circumference of a circle (places for leaves or kernels) are occupied, advancing invariably by the same place number $k$, that is to say: with an unchanging rotation angle. If $n$ and $k$ are Fibonacci-numbers, amazing patterns appear in the sequence of the respective minimal distance between the positions occupied up to that time.},
msc2010 = {F65xx (D55xx)},
identifier = {2009e.00389},
}