## Osaka Journal of Mathematics

### On the digital representation of integers with bounded prime factors

Yann Bugeaud

#### Abstract

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

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

Dates
First available in Project Euclid: 18 April 2018

https://projecteuclid.org/euclid.ojm/1524038730

Mathematical Reviews number (MathSciNet)
MR3787747

Zentralblatt MATH identifier
06870391

#### Citation

Bugeaud, Yann. On the digital representation of integers with bounded prime factors. Osaka J. Math. 55 (2018), no. 2, 315--324. https://projecteuclid.org/euclid.ojm/1524038730

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