Yuchen Ding

collaborators

6 papers

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

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…