Lucas sequences, Pell's equations, and automorphisms of K3 surfaces
Kwangwoo Lee
TL;DR
This paper explores the relationships between Lucas sequences, Pell's equations, and automorphisms of K3 surfaces with Picard number 2, using these links to analyze intersections of Lucas sequences.
Contribution
It establishes new correspondences connecting Lucas sequences, Pell's equations, and K3 surface automorphisms, enabling intersection analysis of Lucas sequences.
Findings
Identified correspondences between Lucas sequences and Pell's equations.
Determined intersections of specific Lucas sequences.
Linked automorphisms of K3 surfaces to number sequences.
Abstract
We have the correspondences between Lucas sequences, Pell's equations, and the automorphisms of K3 surfaces with Picard number 2. Using these correspondences, we determine the intersections of some Lucas sequences.
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Taxonomy
TopicsAdvanced Mathematical Theories and Applications · Commutative Algebra and Its Applications · Algebraic Geometry and Number Theory