Wouter van Doorn

collaborators

19 papers

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 ErdÅs, we prove th…

math.NT2026

Gaps in Multiplicative Sidon Sets II

Wouter van Doorn, Quanyu Tang

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

math.NT2026

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<\…

math.NT2026

Resolution of two conjectures by ErdÅs and Hall concerning separable numbers

Stijn Cambie, Wouter van Doorn

ErdÅs and Hall defined a pair $(m, n)$ of positive integers to be interlocking, if between any pair of consecutive divisors (both larger than $1$ ) of $n$ (resp. $m$ ) there is a di…

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…

On Some Problems from the Kourovka Notebook

Consecutive integers free of certain prime factors

Gaps in Multiplicative Sidon Sets II

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

Resolution of two conjectures by ErdÅs and Hall concerning separable numbers

Three-term arithmetic progressions of consecutive powerful numbers

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

Resolution of two conjectures by ErdÅs and Hall concerning separable numbers