On Pillai's Problem involving Lucas sequences of the second kind

2023/09/20 by Heintze, Sebastian, Ziegler, Volker
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2309.11173

Abstract

In this paper we consider the Diophantine equation V_n - b^m = c for given integers b,c with b ≥ 2 , whereas V_n varies among Lucas-Lehmer sequences of the second kind. We prove under some technical conditions that if the considered equation has at least three solutions (n,m) , then there is an upper bound on the size of the solutions as well as on the size of the coefficients in the characteristic polynomial of V_n .

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