Osaka Journal of Mathematics

On the digital representation of integers with bounded prime factors

Yann Bugeaud

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Let $b \ge 2$ 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 $b$.

Article information

Osaka J. Math., Volume 55, Number 2 (2018), 315-324.

First available in Project Euclid: 18 April 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11A63: Radix representation; digital problems {For metric results, see 11K16} 11J86: Linear forms in logarithms; Baker's method 11J87: Schmidt Subspace Theorem and applications


Bugeaud, Yann. On the digital representation of integers with bounded prime factors. Osaka J. Math. 55 (2018), no. 2, 315--324.

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