W. V. van Doorn

activity

20242026

collaborators

10 papers

math.NT2026

The shortest harmonic sums with decreasing denominator

Wouter van Doorn

For a positive integer $a$ , let $b (a)$ be the smallest integer $b > a$ such that the denominator of $\frac{1}{a} + \frac{1}{a + 1} + \dots + \frac{1}{b}$ is smaller than the denomin…

math.GR2026

On Some Problems from the Kourovka Notebook

Wouter van Doorn, Elias Judin, Pietro Monticone +1

The Kourovka Notebook is a long-running collection of open problems in group theory. In this paper we present solutions to eight of its problems. We construct a group with exactly…

math.NT2026

Consecutive integers free of certain prime factors

Wouter van Doorn, Quanyu Tang

Let $n_{k}$ denote the least integer $n > 2 k$ such that $(n - k) (n - k + 1) \dots (n - 1)$ is not divisible by any prime in the interval $(k, 2 k)$ . Confirming a conjecture of Erdős, we prove tha…

math.NT2026

Gaps in Multiplicative Sidon Sets II

Wouter van Doorn, Quanyu Tang

With $ρ = \frac{13 - 69}{10} \approx 0.47$ , it was recently established that there exist multiplicative Sidon sets (sets without any non-trivial solutions to $ab = c d$ ) in $\{1…

math.NT2026

Three-term arithmetic progressions of consecutive powerful numbers

Wouter van Doorn

We show that infinitely many three-term arithmetic progressions $N, N + d, N + 2 d$ of powerful numbers exist with $d = 2 N + 1$ . We further conjecture that infinitely many of the…

math.NT2025

The smallest denominator not contained in a unit fraction decomposition of $1$ with fixed length

Wouter van Doorn, Quanyu Tang

Let $v (k)$ be the smallest integer larger than $1$ that does not occur among the denominators in any identity of the form $1 = \frac{1}{n _{1}} + \dots + \frac{1}{n _{k}},$ where $1 \le n_1<\…

The shortest harmonic sums with decreasing denominator

On Some Problems from the Kourovka Notebook

Consecutive integers free of certain prime factors

Gaps in Multiplicative Sidon Sets II

Three-term arithmetic progressions of consecutive powerful numbers

The smallest denominator not contained in a unit fraction decomposition of 1 with fixed length

The smallest denominator not contained in a unit fraction decomposition of $1$ with fixed length