Yuchen Ding

activity

20222026

collaborators

16 papers

math.NT2026

A Romanoff-type theorem for $P_{2}$ +{ $a^{a}$ : a $\geq$ 1}

Yuchen Ding, Huixi Li, Junfeng Li

Let $Ω (n)$ denote the number of prime factors of $n$ , counted with multiplicity, and put $P_{2}$ ={ $m$ $\geq$ 1: $Ω (m)$ $\leq$ 2}. We prove that the sumset $P_{2}$ +{ $a^{a}$ : a $\geq$ 1} has po…

math.NT2026

Dense finite Sidon sets on arithmetic progressions

Yuchen Ding

Let $S \subset {1, 2, \dots, n}$ be a Sidon set with $∣ S ∣ = n^{1/2} + O (n^{1/2 - δ})$ for some fixed $δ > 0$ . This article provides the following expected asymptotic formula $$ \sum_{\subst…

math.NT2026

An AI Proof of 18-Variable Undecidability for Diophantine Equations over $Z [i]$

Yuchen Ding, Junfeng Li

This paper presents an AI proof that there is no algorithm deciding whether a polynomial equation over the Gaussian integers in $18$ unknowns has a solution. The proof improves the…

math.NT2026

Adjacent comparison bounds and extremal sets for Ruzsa numbers

Yuchen Ding, Huixi Li, Junfeng Li +2

Let $m$ be a positive integer and $Z_{m}$ the residue class ring modulo $m$ . The Ruzsa number $R_{m}$ is defined to be the least integer $r$ such that there is a subset $\math…

math.NT2026

Note on unique representation bases

Yuchen Ding, Jie Wang

Answering affirmatively a 2007 problem of Chen, the first author proved that there is a unique representation basis $A$ of $Z$ and a constant $c > 0$ such that $$ A(-x,x)\ge…

math.NT2025

Note on shifted primes with large prime factors

Yuchen Ding, Zhiwei Wang

We denote by $P^{+} (n)$ the largest prime factor of the integer $n$ . In 1935, Erd\H os studied the quantity $T_{c} (x)$ defined by $$ T_c(x)=\big|\big\{p\le x: P^+(p-1)\ge p^c\big\}\big…

math.NT2025

The Diophantine Frobenius Problem revisited

Yuchen Ding, Weijia Wang, Hao Zhang

Let $k \geq 2$ and $a_{1}, a_{2}, \dots, a_{k}$ be positive integers with \[ \gcd(a_1, a_2, \cdots, a_k)=1. \] It is proved that there exists a positive integer $G_{a_1, a_2, \cdots, a_k}…

math.NT2025

Note on a conjecture of Sárközy on special sequences

Yuchen Ding, Huixi Li, Zihan Zhang

Let $α > 1$ be an irrational number and $k \geq 2$ a positive integer. Let $f (x)$ be a polynomial with positive integer coefficients. Solving a 2001 problem of Sárközy on special seque…

math.NT2025

Note on a problem of Sárközy on multiplicative representation functions

Yuchen Ding

Motivated by a 2001 problem of Sárközy, we classify all situations of the integers $b, c, e$ and $f$ satisfying \begin{align*} \limsup_{n\rightarrow\infty}|d(\mathcal{A},bn+c)-d(\mat…

math.NT2025

On two Romanoff type problems of Erdős

Yuchen Ding

Let $P$ be the set of primes and, for $a > 1$ , put $S_{a} = p + ⌊ a^{k} ⌋ : p \in P, k \geq 1$ . Erdős recorded a question of Kalm'ar asking whether $\mat…

math.NT2025

Note on a theorem of Birch and Erdős

Yuchen Ding, Honghu Liu, Zi Wang

Let $p, q > 1$ be two relatively prime integers and $N$ the set of nonnegative integers. Let $f_{p, q} (n)$ be the number of different expressions of $n$ written as a sum of di…

math.NT2024

Note on a conjecture of Ram\'ırez Alfons\'ın and Skałba

Tianhan Dai, Yuchen Ding, Hui Wang

Let $2 < a < b$ be two relatively prime integers and $g = ab - a - b$ . It is proved that there exists at least one prime $p \leq g$ of the form $p = a x + b y (x, y \in Z_{\geq 0})$ , which co…

math.NT2024

A generalization of the Romanoff theorem

Yuchen Ding, Wenguang Zhai

Let $P$ be the set of primes and $N$ the set of positive integers. Let also $r_{1}, ..., r_{t}$ be positive real numbers and $R_{2} (r_{1}, ..., r_{t})$ the set of odd integers…

math.NT2023

On a conjecture of Ram\'ırez Alfons\'ın and Skałba III

Yuchen Ding, Takao Komatsu

Let $1 < c < d$ be two relatively prime integers. For a non-negative integer $ℓ$ , let $g_{ℓ} (c, d)$ be the largest integer $n$ such that $n = c x + d y$ has at most $ℓ$ non-negative…

math.NT2023

On a conjecture of Ram\'ırez Alfons\'ın and Skałba II

Yuchen Ding, Wenguang Zhai, Lilu Zhao

Let $1 < c < d$ be two relatively prime integers and $g_{c, d} = c d - c - d$ . We confirm, by employing the Hardy--Littlewood method, a 2020 conjecture of Ram\'ırez Alfons\'ın and Skałba which…

math.NT2022

On a conjecture of R. M. Murty and V. K. Murty II

Yuchen Ding, Victor Zhenyu Guo, Yu Zhang

Let $ω^{*} (n)$ be the number of primes $p$ such that $p - 1$ divides $n$ . Assuming the Elliott--Halberstam Conjecture, we prove a conjecture posted by M. R. Murty and V. K. Murty in 20…

A Romanoff-type theorem for P2​+{aa: a≥ 1}

Dense finite Sidon sets on arithmetic progressions

An AI Proof of 18-Variable Undecidability for Diophantine Equations over Z[i]

Adjacent comparison bounds and extremal sets for Ruzsa numbers

Note on unique representation bases

Note on shifted primes with large prime factors

The Diophantine Frobenius Problem revisited

Note on a conjecture of Sárközy on special sequences

Note on a problem of Sárközy on multiplicative representation functions

On two Romanoff type problems of Erdős

Note on a theorem of Birch and Erdős

Note on a conjecture of Ram\'ırez Alfons\'ın and Skałba

A generalization of the Romanoff theorem

On a conjecture of Ram\'ırez Alfons\'ın and Skałba III

On a conjecture of Ram\'ırez Alfons\'ın and Skałba II

On a conjecture of R. M. Murty and V. K. Murty II

A Romanoff-type theorem for $P_{2}$ +{ $a^{a}$ : a $\geq$ 1}

An AI Proof of 18-Variable Undecidability for Diophantine Equations over $Z [i]$