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INTERNATIONAL JOURNAL OF MATHEMATICAL MODELS AND METHODS IN APPLIED SCIENCES Spectrum of Fibonacci and Lucas numbers

By Asker Ali Abiyev

Abstract

Abstract It has been achieved polynomial function, depending on arguments a + b and ab arguments of expression a n +b n for the biggest and smallest numbers which are in the centre of natural geometrical figures (line, square, cube,…,hypercube). The coefficients of this polynomial are defined from triangle tables, written by special algorithm by us. The sums of the numbers in each row of the triangles make Lucas and Fibonacci sequences. New formulae for terms of these sequences have been suggested by us (Abiyev’s theorem). As the coefficients of the suggested polynomial are spectrum of Fibonacci and Lucas numbers they will opportunity these number’s application field to be enlarged

Topics: Lucas, Fibonacci, sequences, identity, Binet formula
Year: 2013
OAI identifier: oai:CiteSeerX.psu:10.1.1.352.5709
Provided by: CiteSeerX
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