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arXiv · 1704.00432

On the digital representation of smooth numbers

Yann Bugeaud·Hajime Kaneko
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Abstract

Let $b \ge 2$ be an integer. Among other results, we establish, in a quantitative form, that any sufficiently large integer which is not a multiple of $b$ cannot have simultaneously only few distinct prime factors and only few nonzero digits in its representation in base $b$.

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Yann Bugeaud, Hajime Kaneko. 2017-04-03. On the digital representation of smooth numbers. https://doi.org/10.1017/s0305004117000640

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