On b−repdigits which are sums of three Narayana numbers with a consequence

Authors

• University of Kara, Kara, Togo
• Pagdame Tiebekabe
• S´emou Diouf Cheikh
• Anta Diop University, Dakar, Senegal
• Salifou Nikiema
• L´ed´ea Bernard Ou´edraogo University (ULBO), Somiaga, Burkina Faso

Page

258-272

Abstract

The sequence known as Narayana’s cows sequence is defined by the thirdorder linear recurrence relation Nn = Nn−1 + Nn−3, for n ≥ 3, with the initial values given by N0 = N1 = N2 = 1. In this paper, we explore the class of numbers known as brepdigits that can be represented as the sum of three terms from this sequence. Specifically, we aim to identify all such numbers for bases in the range 2 ≤ b ≤ 30. Our approach relies on precise lower bounds for linear forms in logarithms, along with an enhanced version of the Baker-Davenport reduction method applied to Diophantine equations.

Recommended Citation

University of Kara, Kara, Togo; Tiebekabe, Pagdame; Diouf Cheikh, S´emou; Anta Diop University, Dakar, Senegal; Nikiema, Salifou; and L´ed´ea Bernard Ou´edraogo University (ULBO), Somiaga, Burkina Faso (2025) "On b−repdigits which are sums of three Narayana numbers with a consequence," Baku Mathematical Journal: Vol. 4: Iss. 2, Article 10.
DOI: 10.32010/j.bmj.2025.19
Available at: https://www.bakumathj.org/home/vol4/iss2/10