$k$-Fibonacci numbers which are Narayana's cows numbers

TL;DR

This paper characterizes all generalized Fibonacci numbers that are also Narayana's cows numbers, using advanced number theory techniques to identify these special intersections.

Contribution

It provides a complete classification of generalized Fibonacci numbers that coincide with Narayana's cows numbers, employing Baker's theory and reduction methods.

Findings

Identified all generalized Fibonacci numbers that are Narayana's cows numbers.

Used Baker's theory of linear forms in logarithms for proofs.

Applied Baker-Davenport reduction method to refine results.

Abstract

In this paper,we find all generalized Fibonacci numbers which are Narayana's cows numbers. In our proofs, we use both Baker's theory of nonzero linear forms in logarithms of algebraic numbers and the Baker-Davenport reduction method.