Yuchen Ding

activity

20182024

most citedOn a conjecture on shifted primes with large prime factors, II

1 citations · 1 across the 12 of their papers we have counts for

collaborators

13 papers

math.NT2024

On a problem of Nathanson on non-minimal additive complements

Shi--Qiang Chen, Yuchen Ding

Let $C$ and $W$ be two sets of integers. If $C + W = Z$ , then $C$ is called an additive complement to $W$ . We further call $C$ a minimal additive complement to $W$ if no prope…

math.NT2024★ 1 cited

On a conjecture on shifted primes with large prime factors, II

Yuchen Ding

Let $P$ be the set of primes and $π (x)$ the number of primes not exceeding $x$ . Let also $P^{+} (n)$ be the largest prime factor of $n$ with convention $P^{+} (1) = 1$ and $$ T_c…

math.NT2023

A new upper bound on Ruzsa's number on the Erd\H os-Turán conjecture

Yuchen Ding, Lilu Zhao

In this note, we show that the Ruzsa number $R_{m}$ is bounded by $192$ for any positive integer $m$ , which improved the prior bound $R_{m} \leq 288$ given by Y.--G. Chen in 2008.

math.NT2023

Solution to a problem of Luca, Menares and Pizarro-Madariaga

Yuchen Ding, Lilu Zhao

Let $k \geq 2$ be a positive integer and $P^{+} (n)$ the greatest prime factor of a positive integer $n$ with convention $P^{+} (1) = 1$ . For any $θ\in \left[\frac 1{2k},\frac{17}{32k}\right…

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_…

math.NT2022

On a conjecture on shifted primes with large prime factors

Yuchen Ding

Let $P$ be the set of all primes and $π (x)$ be the number of primes up to $x$ . For any $n \geq 2$ , let $P^{+} (n)$ be the largest prime factor of $n$ . For $0 < c < 1$ , let $$T_c(x…

math.NT2022

On three problems of Y.--G. Chen

Yuchen Ding

In this short note, we answer two questions of Chen and Ruzsa negatively and answer a problem of Ma and Chen affirmatively.

math.NT2022

A counterexample of two Romanov type conjectures

Yuchen Ding

In this note, we disprove two Romanov type conjectures posed by Chen.

math.NT2022

Sum of elements in finite Sidon sets II

Yuchen Ding

A set $S \subset {1, 2, ..., n}$ is called a Sidon set if all the sums $a + b (a, b \in S)$ are different. Let $S_{n}$ be the largest cardinality of the Sidon sets in ${1, 2, ..., n}$ . In a…

math.NT2022

Quantitative results of the Romanov type representation functions

Yong-Gao Chen, Yuchen Ding

For $α > 0$ , let $A = {a_{1} < a_{2} < a_{3} < \dots}$ and $L = {ℓ_{1}, ℓ_{2}, ℓ_{3}, \dots} (not necessarily different)$ be two sequences of positive…

math.NT2022

On a conjecture of Erdős

Yong-Gao Chen, Yuchen Ding

Let $P$ denote the set of all primes. In 1950, P. Erdős conjectured that if $c$ is an arbitrarily given constant, $x$ is sufficiently large and $a_{1}, \dots, a_{t}$ are posi…

math.NT2022

On a problem of Romanoff type

Yuchen Ding

Let $P$ and $N$ be the sets of all primes and natural numbers, respectively. In this article, it is proved that there has a positive lower density of the natural…

math.NT2018

A note on the sum of reciprocals

Yuchen Ding, Yu-Chen Sun

For a fixed positive integer $m$ and any partition $m = m_{1} + m_{2} + \dots + m_{e}$ , there exists a sequence ${n_{i}}_{i = 1}^{k}$ of positive integers such that $$m=\frac{1}{n_{1}}…