A UNIFIED WAY FOR OBTAINING DIVIDING FORMULAS ${\bf n|Q(n)}$

Abstract

We show that interesting dividing formulas such as, Chinese theorem, Fermat's little theorem, and Euler's theorem can easily be derived from some well-known iterated maps. Other dividing formulas concerning Fibonacci numbers, generalized Fibonacci numbers of degree m, and numbers of other types can also be derived. The results show that iterated maps offer a systematic and unified way for obtaining nontrivial dividing formulas $n|Q(n)$, and we can thus understand the dividing formulas from the point of view of iterated maps.