Quan-Hui Yang

activity

20112026

h

-fold sumsets

9 citations · 10 across the 19 of their papers we have counts for

collaborators

22 papers

math.CO2026

On additive complements in natural numbers

Quan-Hui Yang, Lilu Zhao

We prove that for additive complements $A$ and $B$ , if $x \to + \infty lim sup \frac{A ( x ) B ( x )}{x} < \frac{4}{3},$ then $A (x) B (x) - x \to + \infty (x \to + \infty) .$ This impro…

math.CO2026

Products of Two Integers Avoiding Perfect Powers

Quan-Hui Yang, Lilu Zhao

For integers $d \geq 3$ , let $F_{2, d} (n)$ be the largest size of a subset of $[n]$ containing no two distinct elements whose product is a perfect $d$ -th power, and let $f_{2, d} (n)$ …

math.NT2023

On monotone increasing representation functions

Sándor Z. Kiss, Csaba Sándor, Quan-Hui Yang

Let $k \geq 2$ be an integer and let $A$ be a set of nonnegative integers. The representation function $R_{A, k} (n)$ for the set $A$ is the number of representations of a nonnegative…

math.NT2023

On a problem of Nathanson related to minimal asymptotic bases of order $h$

Shi-Qiang Chen, Csaba Sándor, Quan-Hui Yang

For integer $h \geq 2$ and $A \subseteq N$ , we define $h A$ to be all integers which can be written as a sum of $h$ elements of $A$ . The set $A$ is called an asymptotic basis o…

math.NT2021

Note on a problem of Nathanson related to the $φ$ -Sidon set

Csaba Sándor, Quan-Hui Yang, Jun-Yu Zhou

Let $φ (x_{1}, \dots, x_{h}) = c_{1} x_{1} + \dots + c_{h} x_{h}$ be a linear form with coefficients in a field $F$ , and let $V$ be a vector space over $F$ . A nonempty…

math.NT2021

On a discriminator for the polynomial $f (x) = x^{3} + x$

Quan-Hui Yang, Lilu Zhao

Let $Δ (n)$ denote the smallest positive integer $m$ such that $a^{3} + a (1 \leq a \leq n)$ are pairwise distinct modulo $m$ . The purpose of this paper is to determine $Δ (n)$ for all positi…

math.NT2021

On the integer sets with the same representation functions

Kai-Jie Jiao, Csaba Sándor, Quan-Hui Yang +1

Let $N$ be the set of all nonnegative integers. For $S \subseteq N$ and $n \in N$ , let $R_{S} (n)$ denote the number of solutions of the equation $n = s_{1} + s_{2}$ ,…

math.NT2021

On a conjecture of Sun involving powers of three

Quan-Hui Yang, Lilu Zhao

Given a positive integer $n \geq 2$ , let $D (n)$ denote the smallest positive integer $m$ such that $a^{3} + a (1 \leq a \leq n)$ are pairwise distinct modulo $m^{2}$ . A conjecture of Z.-W. Sun…

math.NT2020

On the structure of the $h$ -fold sumsets

Jun-Yu Zhou, Quan-Hui Yang

Let~ $A$ be a set of nonnegative integers. Let~ $(h A)^{(t)}$ be the set of all integers in the sumset~ $h A$ that have at least~ $t$ representations as a sum of~ $h$ elements of~ $A$ . In…

math.NT2019

A note on the lower bound of representation functions

Xing-Wang Jiang, Csaba Sandor, Quan-Hui Yang

For a set $A$ of nonnegative integers, let $R_{2} (A, n)$ denote the number of solutions to $n = a + a^{'}$ with $a, a^{'} \in A$ , $a < a^{'}$ . Let $A_{0}$ be the Thue-Morse sequence and $B_0=\mathbb{N}\…

math.NT2019

On the values of representation functions II

Xing-Wang Jiang, Csaba Sandor, Quan-Hui Yang

For a set $A$ of nonnegative integers, let $R_{2} (A, n)$ and $R_{3} (A, n)$ denote the number of solutions to $n = a + a^{'}$ with $a, a^{'} \in A$ , $a < a^{'}$ and $a \leq a^{'}$ , respectively. In this paper…

math.NT2017

Powerful numbers in $(1^{ℓ} + q^{ℓ}) (2^{ℓ} + q^{ℓ}) \dots (n^{ℓ} + q^{ℓ})$

Quan-Hui Yang, Qing-Qing Zhao

Let $q$ be a positive integer. Recently, Niu and Liu proved that if $n \geq max {q, 1198 - q}$ , then the product $(1^{3} + q^{3}) (2^{3} + q^{3}) \dots (n^{3} + q^{3})$ is not a powerful number. In this…

math.NT2017

On a conjecture of Erdős about sets without $k$ pairwise coprime integers

Sándor Z. Kiss, Csaba Sándor, Quan-Hui Yang

Let $Z^{+}$ be the set of positive integers. Let $C_{k}$ denote all subsets of $Z^{+}$ such that neither of them contains $k + 1$ pairwise coprime integers and $C…

math.NT2017

On some properties of representation functions related to the Erdős-Turán conjecture

Csaba Sándor, Quan-Hui Yang

For a set $A \subseteq N$ and $n \in N$ , let $R_{A} (n)$ denote the number of ordered pairs $(a, a^{'}) \in A \times A$ such that $a + a^{'} = n$ . The celebrated Erdős-Turán conjec…

math.NT2017

On minimal additive complements of integers

Sándor Z. Kiss, Csaba Sándor, Quan-Hui Yang

Let $C, W \subseteq Z$ . If $C + W = Z$ , then the set $C$ is called an additive complement to $W$ in $Z$ . If no proper subset of $C$ is an additive complement t…

math.NT2016

A lower bound of Ruzsa's number related to the Erdős-Turán conjecture

Csaba Sándor, Quan-Hui Yang

For a set $A \subseteq N$ and $n \in N$ , let $R_{A} (n)$ denote the number of ordered pairs $(a, a^{'}) \in A \times A$ such that $a + a^{'} = n$ . The celebrated Erdős-Turán conjec…

math.NT2015★ 1 cited

On the sumsets of exceptional units in $Z_{n}$

Quan-Hui Yang, Qing-Qing Zhao

Let $R$ be a commutative ring with $1 \in R$ and $R^{*}$ be the multiplicative group of its units. In 1969, Nagell introduced the exceptional unit $u$ if both $u$ and $1 - u$ belon…

math.NT2014★ 9 cited

On the cardinality of general $h$ -fold sumsets

Quan-Hui Yang, Yong-Gao Chen

Let $A = {a_{0}, a_{1}, \dots, a_{k - 1}}$ be a set of $k$ integers. For any integer $h \geq 1$ and any ordered $k$ -tuple of positive integers $r = (r_{0}, r_{1}, \dots, r_{k - 1})$ , we defin…

math.NT2014

Proof of a conjecture related to divisibility properties of binomial coefficients

Quan-Hui Yang

Let $a, b$ and $n$ be positive integers with $a > b$ . In this note, we prove that $(2 bn + 1) (2 bn + 3) (bn 2 bn) 3 (a - b) (3 a - b) (an 2 an) (bn an) .$ This confirms a r…

math.NT2012

Density of integral sets with missing differences

Quan-Hui Yang, Min Tang

Motzkin posed the problem of finding the maximal density $μ (M)$ of sets of integers in which the differences given by a set $M$ do not occur. The problem is already settled when $|…

math.NT2012

Weighted representation functions on $Z_{m}$

Quan-Hui Yang, Yong-Gao Chen

Let $m$ , $k_{1}$ , and $k_{2}$ be three integers with $m \geq 2$ . For any set $A \subseteq Z_{m}$ and $n \in Z_{m}$ , let $r^_{k_{1}, k_{2}} (A, n)$ denote the number of solution…

math.NT2011

An identity on the $2 m$ -th power mean value of the generalized Gauss sums

Feng Liu, Quan-Hui Yang

In this paper, using combinatorial and analytic methods, we prove an exact calculating formula on the $2 m$ -th power mean value of the generalized quadratic Gauss sums for $m \geq 2$ …

On additive complements in natural numbers

Products of Two Integers Avoiding Perfect Powers

On monotone increasing representation functions

On a problem of Nathanson related to minimal asymptotic bases of order h

Note on a problem of Nathanson related to the φ-Sidon set

On a discriminator for the polynomial f(x)=x3+x

On the integer sets with the same representation functions

On a conjecture of Sun involving powers of three

On the structure of the h-fold sumsets

A note on the lower bound of representation functions

On the values of representation functions II

Powerful numbers in (1ℓ+qℓ)(2ℓ+qℓ)⋯(nℓ+qℓ)

On a conjecture of Erdős about sets without k pairwise coprime integers

On some properties of representation functions related to the Erdős-Turán conjecture

On minimal additive complements of integers

A lower bound of Ruzsa's number related to the Erdős-Turán conjecture

On the sumsets of exceptional units in Zn​

On the cardinality of general h-fold sumsets

Proof of a conjecture related to divisibility properties of binomial coefficients

Density of integral sets with missing differences

Weighted representation functions on Zm​

An identity on the 2m-th power mean value of the generalized Gauss sums

On a problem of Nathanson related to minimal asymptotic bases of order $h$

Note on a problem of Nathanson related to the $φ$ -Sidon set

On a discriminator for the polynomial $f (x) = x^{3} + x$

On the structure of the $h$ -fold sumsets

Powerful numbers in $(1^{ℓ} + q^{ℓ}) (2^{ℓ} + q^{ℓ}) \dots (n^{ℓ} + q^{ℓ})$

On a conjecture of Erdős about sets without $k$ pairwise coprime integers

On the sumsets of exceptional units in $Z_{n}$

On the cardinality of general $h$ -fold sumsets

Weighted representation functions on $Z_{m}$

An identity on the $2 m$ -th power mean value of the generalized Gauss sums