Taiwanese Journal of Mathematics

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

Chyi-Lung Lin

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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


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