## Taiwanese Journal of Mathematics

- Taiwanese J. Math.
- Volume 2, Number 4 (1998), 469-481.

### 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.

#### Article information

**Source**

Taiwanese J. Math., Volume 2, Number 4 (1998), 469-481.

**Dates**

First available in Project Euclid: 18 July 2017

**Permanent link to this document**

https://projecteuclid.org/euclid.twjm/1500407018

**Digital Object Identifier**

doi:10.11650/twjm/1500407018

**Mathematical Reviews number (MathSciNet)**

MR1662948

**Zentralblatt MATH identifier**

0922.11015

**Subjects**

Primary: 11B83: Special sequences and polynomials 11B39: Fibonacci and Lucas numbers and polynomials and generalizations 11A99: None of the above, but in this section

**Keywords**

iterated maps dividing formulas fixed points $n$-periods $n$-cycles

#### Citation

Lin, Chyi-Lung. A UNIFIED WAY FOR OBTAINING DIVIDING FORMULAS ${\bf n|Q(n)}$. Taiwanese J. Math. 2 (1998), no. 4, 469--481. doi:10.11650/twjm/1500407018. https://projecteuclid.org/euclid.twjm/1500407018