IJPAM: Volume 53, No. 4 (2009)

FIBONACCI-LIKE POLYNOMIALS: COMPUTATIONAL
EXPERIMENTS, PROOFS, AND CONJECTURES

Sergei Abramovich$^1$, Gennady A. Leonov$^2$
$^1$School of Education and Professional Studies
State University of New York
44, Potsdam Pierrepont Ave., Potsdam, NY 13676-2294, USA
e-mail: [email protected]
$^2$Faculty of Mathematics and Mechanics
St. Petersburg State University
Universitetskyi, 28, Peterhof, St. Petersburg, 198504, RUSSIA
e-mail: [email protected]


Abstract.This article introduces a new class of polynomials arising in a course of exploring a qualitative behavior of orbits of a two-parametric difference equation. The use of symbolic computations and computational experiments in the context of Maple made it possible to prove polynomial generalizations of Cassini's identity for Fibonacci numbers and formulate conjectures about polynomial forms of Catalan's identity.

Received: May 9, 2009

AMS Subject Classification: 12-04, 11C08

Key Words and Phrases: Fibonacci-like polynomials, Cassini's identity, Catalan's identity, Maple

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 53
Issue: 4