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arXiv · 2601.16972

On the length of an interval that contains distinct multiples of the first $n$ positive integers

Wouter van Doorn
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Abstract

Confirming a conjecture by Erd\H os and Pomerance, we prove that there exist intervals of length $\frac{cn\log n}{\log \log n}$ that do not contain distinct multiples of $1, 2, \ldots, n$.

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Wouter van Doorn. 2026-01-23. On the length of an interval that contains distinct multiples of the first $n$ positive integers. https://doi.org/10.5281/zenodo.18154085

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