IJPAM: Volume 90, No. 3 (2014)

THE PERIOD MODULO PRODUCT OF
CONSECUTIVE FIBONACCI NUMBERS

Narissara Khaochim$^1$, Prapanpong Pongsriiam$^2$
$^{1,2}$Department of Mathematics, Faculty of Science
Silpakorn University
Ratchamankanai Rd, Nakornpathom, 73000, THAILAND


Abstract. Let $F_{n}$ be the $n$th Fibonacci number. The period modulo $m$, denoted by $s(m)$, is the smallest positive integer $k$ for which $F_{n+k}\equiv F_{n}\pmod m$ for all $n\geq0$. In this paper, we find the period modulo product of consecutive Fibonacci numbers. For instance, we prove that, for $n\geq1$,




Received: September 5, 2013

AMS Subject Classification: 11B39

Key Words and Phrases: Fibonacci sequence, divisibility, Fibonacci entry point, the period modulo $m$

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DOI: 10.12732/ijpam.v90i3.7 How to cite this paper?
Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2014
Volume: 90
Issue: 3