Quanyu Tang

activity

20242026

collaborators

Showing math.NTShow all

6 papers · 1 filter

math.NT2026

A counterexample to a conjecture of Sárközy on sums and products modulo a prime

Quanyu Tang

Let $p$ be a prime and, for $A \subseteq F_{p}$ , define $A^{*} = (A + A) \cup (AA)$ . Sárközy conjectured that there exist constants $c > 0$ and $p_{0}$ such that, for every prime $p>p_…

math.NT2026

Average first-passage times for character sums

Quanyu Tang, Hao Zhang

Let $ε > 0$ and, for an odd prime $p$ , set $S_{ℓ} (p) := n \leq ℓ \sum (\frac{n}{p}) .$ Define the first-passage time $$ f_\varepsilon(p):=\min\{\ell\ge 1:\ S…

math.NT2025

Harmonic LCM patterns and sunflower-free capacity

Quanyu Tang, Shengtong Zhang

Fix an integer $k \geq 3$ . Call a set $A \subseteq [N]$ LCM- $k$ -free if it does not contain distinct $a_{1}, \dots, a_{k}$ such that $lcm (a_{i}, a_{j})$ is the same for all $1\le i<j\le…

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<\…

math.NT2025

An improved lower bound for Erdős--Szekeres products

Quanyu Tang

In 1959, Erdős and Szekeres posed a series of problems concerning the size of polynomials of the form $P_{n} (z) = j = 1 \prod n (1 - z^{s_{j}}),$ where $s_{1}, \dots, s_{n}$ are positi…

math.NT2025

On a conjecture of Erdős and Graham about the Sylvester's sequence

Zheng Li, Quanyu Tang

Let ${u_{n}}_{n = 1}^{\infty}$ be the Sylvester's sequence (sequence A000058 in the OEIS), and let $a_{1} < a_{2} < \dots$ be any other positive integer sequence satisfying $ \sum_{i=…

A counterexample to a conjecture of Sárközy on sums and products modulo a prime

Average first-passage times for character sums

Harmonic LCM patterns and sunflower-free capacity

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

An improved lower bound for Erdős--Szekeres products

On a conjecture of Erdős and Graham about the Sylvester's sequence

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