Distinct digits in basebexpansions of linear recurrence sequences

摘要

Let (un)nbe a linear recurrence sequence of integers and letb 1 be a natural number. In this paper, we show that under some mild technical assumptions the basebexpansion of |un| has at leastclogn/log lognnon-zero digits whennis large, wherec 0 is a computable constant depending on the initial sequence (un)nandb. Our results complement the results of C.L. Stewart from [9]. Some diophantine applications are also presented.