Solutions to a Pillai-type equation involving Tribonacci numbers and S-units

2024/03/10 by Batte, Herbert, Luca, Florian
#11B39 #11D45 #11D61 #11Y50 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2403.17953

Abstract

Let \T_n\_{n≥ 0} be the sequence of Tribonacci numbers. In this paper, we study the exponential Diophantine equation T_n-2^x3^y=c, for n,x,y∈ ℤ_≥0. In particular, we show that there is no integer c with at least six representations of the form T_n-2^x3^y.

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