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

Author:

Heintze Sebastian,Ziegler VolkerORCID

Abstract

AbstractIn this paper, we consider the Diophantine equation $$ V_n - b^m = c $$ V n - b m = c for given integers bc with $$ b \ge 2 $$ b 2 , whereas $$ V_n $$ 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 (nm) , 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 $$ V_n $$ V n .

Funder

Austrian Science Fund

Publisher

Springer Science and Business Media LLC

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