Shi-Qiang Chen

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math.NT2026

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

Shi-Qiang Chen, Quan-Hui Yang

Let $h \geq 3$ be an integer and $0 < α < 1/ h$ . In this paper, we prove that there exists a minimal asymptotic basis of order $h$ with asymptotic density $α$ . This solves an open proble…

math.NT2026

On a problem of Nathanson related to minimal asymptotic bases and maximal asymptotic nonbases

Shi-Qiang Chen

Let $N_{0} = {0, 1, 2, \dots}$ and let $h \geq 2$ be an integer. For a set $A \subseteq N_{0}$ , write $h A$ for the set of all sums of $h$ , not necessarily distinct, elements…

math.NT2026

On the size of $h$ -fold sumsets

Shi-Qiang Chen, Quan-Hui Yang

Let $h$ be a positive integer, and let $A$ be a finite set of integers. We derive an exact formula for $∣ h A ∣$ . Furthermore, let $A = {0, 1, \dots, s, a, b}$ , $1 \leq s < a < b$ , and write $…

math.NT2023

Representation functions in the set of natural numbers

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

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 $n = s + s^{'}$ , $s…

math.NT2023

The lower bound of weighted representation function

Shi-Qiang Chen

For any given set $A$ of nonnegative integers and for any given two positive integers $k_{1}, k_{2}$ , $R_{k_{1}, k_{2}} (A, n)$ is defined as the number of solutions of the equation $n=k_1a_1+…

math.NT2023

Correct order on some certain weighted representation functions

Shi--Qiang Chen, Yuchen Ding, Xiaodong Lü +1

Let $N$ be the set of all nonnegative integers. For any positive integer $k$ and any subset $A$ of nonnegative integers, let $r_{1, k} (A, n)$ be the number of solutions $(a_…

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

On a problem of Nathanson related to minimal asymptotic bases and maximal asymptotic nonbases

On the size of h-fold sumsets

Representation functions in the set of natural numbers

The lower bound of weighted representation function

Correct order on some certain weighted representation functions

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

On the size of $h$ -fold sumsets