Abstract

Let $b\ge 2$ be an integer. In this paper we study the base $b$ repdigits that can be expressed as sums or products of Fibonacci and Tribonacci numbers. As a corollary, it is shown that the numbers $1$ and $7$ are the only Mersenne numbers which can be expressed respectively as product and sum of Fibonacci and Tribonacci numbers. This is done using linear forms in logarithms of algebraic numbers (Baker's method) and the Baker-Davenport reduction method (the Dujella-Peth\H {o}'s version).

Keywords: Fibonacci numbers; tribonacci numbers; $b$ repdigits; logarithmic height; reduction method.

DOI: 10.57016/MV-PQCd4362

Pages:  1--12