Yuchen Ding

activity

20222026

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5 papers · 1 filter

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…

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

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

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