Wouter van Doorn

collaborators

4 papers

math.NT2026

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

Wouter van Doorn

Confirming a conjecture by Erd\H os and Pomerance, we prove that there exist intervals of length $\frac{c n l o g n}{l o g l o g n}$ that do not contain distinct multiples of $1, 2, \ld…

math.NT2025

Growth rates of sequences governed by the squarefree properties of its translates

Wouter van Doorn, Terence Tao

We answer several questions of Erdős regarding sequences of natural numbers $A$ whose translates $n + A$ intersect with the squarefree numbers in various specified ways. For instance…

math.NT2025

Smooth sums with small spacings

Wouter van Doorn, Anneroos R. F. Everts

Solving a problem by Erdős, we prove that every positive integer $n$ can be written as a sum $n = b_{1} + b_{2} + \dots + b_{r}$ of distinct $3$ -smooth integers with $1 \le b_{1…

math.NT2025

Improved bounds for the Mayer-Erdős phenomenon on similarly ordered Farey fractions

Wouter van Doorn

Let $\frac{a _{1}}{b _{1}}, \frac{a _{2}}{b _{2}}, \dots$ be the Farey fractions of order $n$ . We then prove that the inequality $(a_{l} - a_{k}) (b_{l} - b_{k}) \geq 0$ holds for all $k$ and $l > k$ w…

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

Growth rates of sequences governed by the squarefree properties of its translates

Smooth sums with small spacings

Improved bounds for the Mayer-Erdős phenomenon on similarly ordered Farey fractions

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