Fibonacci system and residue completeness
Cheng Lien Lang, Mong Lung Lang
TL;DR
This paper establishes precise conditions under which Fibonacci cycles are residue complete, identifying specific moduli where Lucas numbers exhibit this property, thus advancing understanding of Fibonacci residues.
Contribution
It provides necessary and sufficient conditions for Fibonacci cycles to be residue complete, including a complete characterization for Lucas numbers modulo m.
Findings
Lucas numbers modulo m are residue complete if and only if m = 2, 4, 6, 7, 14, or a power of 3.
The paper characterizes when Fibonacci cycles are residue complete (nondefective).
It offers a complete criterion for residue completeness in Fibonacci systems.
Abstract
We give necessary and sufficient conditions for a Fibonacci cycle to be residue complete (nondefective). In particular, the Lucas numbers modulo m is residue complete if and only if m = 2,4,6,7,14 or a power of 3.
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Taxonomy
TopicsAdvanced Mathematical Theories and Applications · Graph theory and applications · Graph Labeling and Dimension Problems