Zeckendorf arithmetic for Lucas numbers
Rachid Chergui
TL;DR
This paper explores algorithms for arithmetic operations on Lucas numbers using Zeckendorf representation, with potential applications in coding theory.
Contribution
It introduces specific algorithms for addition, subtraction, multiplication, and division of Lucas numbers in Zeckendorf form, advancing computational methods in this area.
Findings
Algorithms for basic arithmetic on Lucas numbers in Zeckendorf form are developed.
Potential applications in coding theory are identified.
The methods improve efficiency of computations with Lucas numbers.
Abstract
In this article we will be dedicated some algorithms of addition, subtraction, multiplication and division of two positive integers using Zeckendorf form. Such results find application in coding theory.
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Taxonomy
TopicsAdvanced Mathematical Theories and Applications · Advanced Mathematical Identities · Analytic Number Theory Research