Lilu Zhao

activity

20082026

most citedSums of four squares of primes

6 citations · 19 across the 20 of their papers we have counts for

collaborators

Showing 2021Show all

6 papers · 1 filter

math.NT2021

On a discriminator for the polynomial $f (x) = x^{3} + x$

Quan-Hui Yang, Lilu Zhao

Let $Δ (n)$ denote the smallest positive integer $m$ such that $a^{3} + a (1 \leq a \leq n)$ are pairwise distinct modulo $m$ . The purpose of this paper is to determine $Δ (n)$ for all positi…

math.NT2021

On a conjecture of Sun involving powers of three

Quan-Hui Yang, Lilu Zhao

Given a positive integer $n \geq 2$ , let $D (n)$ denote the smallest positive integer $m$ such that $a^{3} + a (1 \leq a \leq n)$ are pairwise distinct modulo $m^{2}$ . A conjecture of Z.-W. Sun…

math.NT2021

Translation invariant quadratic forms and dense sets of primes

Lilu Zhao

Let $f (x_{1}, \dots, x_{s})$ be a translation invariant indefinite quadratic form of integer coefficients with $s \geq 10$ . Let $A \subseteq P \cap {1, 2, \dots, X}$ . Le…

math.NT2021

On forms in prime variables

Jianya Liu, Lilu Zhao

Let $F_{1}, \dots, F_{R}$ be homogeneous polynomials of degree $d \geq 2$ with integer coefficients in $n$ variables, and let $F = (F_{1}, \dots, F_{R})$ . Suppose that $F_{1}, \dots, F_{R}$ …

math.NT2021

Representation by sums of unlike powers

Jianya Liu, Lilu Zhao

It is proved that all sufficiently large integers $n$ can be represented as $n = x_{1}^{2} + x_{2}^{3} + \dots + x_{13}^{14},$ where $x_{1}, \dots, x_{13}$ are positive integers. This improves upo…

math.CO2021★ 1 cited

Improvements on induced subgraphs of given sizes

Jialin He, Jie Ma, Lilu Zhao

Given integers $m$ and $f$ , let $S_{n} (m, f)$ consist of all integers $e$ such that every $n$ -vertex graph with $e$ edges contains an $m$ -vertex induced subgraph with $f$ edges, and l…

On a discriminator for the polynomial f(x)=x3+x

On a conjecture of Sun involving powers of three

Translation invariant quadratic forms and dense sets of primes

On forms in prime variables

Representation by sums of unlike powers

Improvements on induced subgraphs of given sizes

On a discriminator for the polynomial $f (x) = x^{3} + x$