Members of Narayana's cow sequence that are concatenations of two repdigits

2022/10/03 by Ddamulira, Mahadi, Emong, Paul, Mirumbe, Geoffrey Ismail
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2210.00926

Abstract

Let (N_n)_{n≥ 0} be the Narayana's cow sequence defined by a third-order recurrence relation N₀=0, N₁= N₂=1 , and N_n+3=N_n+2+N_n for all n≥ 0 . In this paper, we determine all Narayana numbers that are concatenations of two repdigits. The proof of our main theorem uses lower bounds for linear forms in logarithms and a version of the Baker-Davenport reduction method in Diophantine approximation.

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