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On the digital representation of integers with bounded prime factors

2016/09/26 by Bugeaud, Yann
#11A63 #11J86 #11J87 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1609.07926

Abstract

Let b ≥ 2 be an integer. Not much is known on the representation in base b of prime numbers or of numbers whose prime factors belong to a given, finite set. Among other results, we establish that any sufficiently large integer which is not a multiple of b and has only small (in a suitable sense) prime factors has at least four nonzero digits in its representation in base b.

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