Generalized Fibonacci numbers and automorphisms of K3 surfaces with Picard number 2

TL;DR

This paper explores the relationship between generalized Fibonacci numbers and automorphisms of K3 surfaces with Picard number 2, establishing new criteria and divisibility properties.

Contribution

It introduces a novel connection between generalized Fibonacci numbers and the automorphism groups of certain K3 surfaces, providing new criteria for Fibonacci numbers.

Findings

Automorphism groups of K3 surfaces with Picard number 2 are characterized using generalized Fibonacci numbers.

A criterion is established for when an integer is a generalized Fibonacci number based on surface automorphisms.

Divisibility of generalized Fibonacci numbers is characterized by divisibility of their indices.

Abstract

Using the properties of generalized Fibonacci numbers, we determine the automorphism groups of some K3 surfaces with Picard number 2. Conversely, using the automorphisms of K3 surfaces with Picard number 2, we prove the criterion for a given integer n is to be a generalized Fibonacci number. Moreover, we show that the generalized k-th Fibonacci number divides the generalized q-th Fibonacci number if and only if k divides q.