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arXiv · 2411.09060

On the distance between factorials and repunits

Michael Filaseta·Florian Luca
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Abstract

We show that if $n\ge n_0$, $b\ge 2$ are integers, $p\ge 7$ is prime and $n!-(b^p-1)/(b-1)\ge 0$, then $n!-(b^p-1)/(b-1) \ge 0.5\log\log n/\log\log\log n$. Further results are obtained, in particular for the case $n!-(b^p-1)/(b-1) < 0$.

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Michael Filaseta, Florian Luca. 2024-11-13. On the distance between factorials and repunits. https://arxiv.org/abs/2411.09060

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