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Bibliographic Details
Main Authors: Filaseta, Michael, Luca, Florian
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2411.09060
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author Filaseta, Michael
Luca, Florian
author_facet Filaseta, Michael
Luca, Florian
contents 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 $n!-(b^p-1)/(b-1) < 0$.
format Preprint
id arxiv_https___arxiv_org_abs_2411_09060
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle On the distance between factorials and repunits
Filaseta, Michael
Luca, Florian
Number Theory
11D61
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 $n!-(b^p-1)/(b-1) < 0$.
title On the distance between factorials and repunits
topic Number Theory
11D61
url https://arxiv.org/abs/2411.09060