Quan-Hui Yang

activity

20172021

collaborators

7 papers

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…

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 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