On the Length of an Interval That Contains Distinct Multiples of the First \(n\) Positive Integers
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 $1, 2, \ldots, n$.
Fields of Study & Subjects
Analytic Number Theory Research
Limits and Structures in Graph Theory
Algebraic Geometry and Number Theory
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 5 January 2026
- Document type
- Preprint