Huixi Li

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20192026

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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

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

An Improvement of Konstantoulas' Density Constant

Huixi Li, Zihan Zhang

Let $A \subset N$ , and define its ordered representation function $r (n) = # {(a, b) \in A \times A : a + b = n} .$ The Erdos--Turan conjecture asserts that, if $r (n) > 0$ for all sufficiently…

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.NT2023

On covering systems of polynomial rings over finite fields

Huixi Li, Biao Wang, Chunlin Wang +1

In 1950, Erdős posed a question known as the minimum modulus problem on covering systems for $Z$ , which asked whether the minimum modulus of a covering system with distinc…

math.NT2023

Some discussions on the Goldbach conjecture

Huixi Li

According to some discussions based on syllogism, we present results on the binary Goldbach conjecture in three categories: results that are weaker than the Goldbach conjecture, su…

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

Adjacent comparison bounds and extremal sets for Ruzsa numbers

An Improvement of Konstantoulas' Density Constant

Note on a conjecture of Sárközy on special sequences

On covering systems of polynomial rings over finite fields

Some discussions on the Goldbach conjecture

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