Repdigits as Product of Fibonacci and Tribonacci Numbers

Dušan Bednařík and Eva Trojovská
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Dušan Bednařík: Department of Mathematics, Faculty of Science, University of Hradec Králové, 50003 Hradec Králové, Czech Republic
Eva Trojovská: Department of Mathematics, Faculty of Science, University of Hradec Králové, 50003 Hradec Králové, Czech Republic

Mathematics, 2020, vol. 8, issue 10, 1-8

Abstract: In this paper, we study the problem of the explicit intersection of two sequences. More specifically, we find all repdigits (i.e., numbers with only one repeated digit in its decimal expansion) which can be written as the product of a Fibonacci by a Tribonacci number (both with the same indexes). To work on this problem, our approach is to combine lower bounds from the Baker’s theory with reduction methods (based on the theory of continued fractions) due to Dujella and Pethö.

Keywords: k -generalized Fibonacci numbers; linear forms in logarithms; reduction method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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