Narayana numbers that are products of two Fibonacci numbers

2025/07/23 by Odjoumani, Japhet
#11B39 #11D61 #11D72 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2508.02688

Abstract

Let \N_m\_m≥0 be the Narayana's cows sequence given by N₀=0, N₁=1=N₂=1 and N_m+3=N_m+2+N_m, for m≥ 0 and let \F_n\_n≥0 be the Fibonacci sequence. In this paper we solve explicitely the Diophantine equation N_m=F_nF_k, in positive unknowns m, n and k. That is, we find the non-zero narayana numbers that are products of two Fibonacci numbers.

Citations

• Repdigits in Narayana's Cows Sequence and their Consequences
• Classical and modular approaches to exponential Diophantine equations. I. Fibonacci and Lucas perfect powers
• A generalization of a theorem of Baker and Davenport

Related

• k-Fibonacci numbers which are Narayana's cows numbers
• Identities involving Narayana numbers
• A Recursion for the FiboNarayana and the Generalized Narayana Numbers
• Members of Narayana's cow sequence that are concatenations of two repdigits
• Narayana Sequence and The Brocard-Ramanujan Equation