On Squares in Lucas Sequences
Francesca Balestrieri
TL;DR
This paper proves, using elementary methods, the conditions under which Lucas sequence terms are not perfect squares, providing new insights into the properties of these sequences.
Contribution
It offers a novel elementary proof for the non-square cases in Lucas sequences, expanding understanding of their algebraic properties.
Findings
Identifies conditions when Lucas sequence terms are not perfect squares
Provides elementary proofs for general cases of non-square Lucas sequence terms
Enhances theoretical understanding of Lucas sequences' algebraic structure
Abstract
In this short paper, we prove, by only using elementary tools, general cases when , where is the Lucas sequence of the first type.
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Taxonomy
TopicsAdvanced Mathematical Theories and Applications · Algebraic Geometry and Number Theory · Analytic Number Theory Research