Pingzhi Yuan

collaborators

6 papers

math.NT2026

A Multiplicative Fourier Proof of the Length-Four Index Conjecture

Hongjian Li, Pingzhi Yuan, Shijie Yuan +1

Let $C_{n}$ be a cyclic group of order $n$ . The index conjecture in zero-sum theory asserts that if $(n, 6) = 1$ , then every minimal zero-sum sequence of length four over $C_{n}$ has inde…

math.NT2025

The order of appearance of the product of the first and second Lucas numbers

Hongjian Li, Huiming Xiao, Pingzhi Yuan

Let $a$ and $b$ be relatively prime integers. Then the first Lucas sequence $(U_{n})_{n \geq 0}$ and the second Lucas sequence $(V_{n})_{n \geq 0}$ are defined respec…

math.NT2025

Faithful Decomposition of Rationals

Sunben Chiu, Pingzhi Yuan, Hongjian Li

If an irreducible fraction $\frac{m}{n} > 0$ can be decomposed into the sum of several irreducible proper fractions with different denominators, and the positive number smaller than $\f…

math.NT2025

Some permutation polynomials via linear translators

Xuan Pang, Pingzhi Yuan, Hongjian Li

Permutation polynomials with explicit constructions over finite fields have long been a topic of great interest in number theory. In recent years, by applying linear translators of…

math.NT2025

On the Elementary Symmetric Functions of ${1, 1/2, \dots, 1/ n} \ {1/ i}$

Weilin Zhang, Hongjian Li, Sunben Chiu +1

In 1946, P. ErdÅs and I. Niven proved that there are only finitely many positive integers $n$ for which one or more of the elementary symmetric functions of $1, 1/2$ , $\cdots, 1…

math.NT2025

On the representation of rational numbers via Euler's totient function

Weilin Zhang, Fengyuan Chen, Hongjian Li +1

Let $b > 1$ be an odd positive integer and $k, l \in N$ . In this paper, we show that every positive rational number can be written as $I ¨ (m^{2}) / (I ¨ (n^{2}))^{b}$ and $Ï(k(m…

A Multiplicative Fourier Proof of the Length-Four Index Conjecture

The order of appearance of the product of the first and second Lucas numbers

Faithful Decomposition of Rationals

Some permutation polynomials via linear translators

On the Elementary Symmetric Functions of {1,1/2,…,1/n}\{1/i}

On the representation of rational numbers via Euler's totient function

On the Elementary Symmetric Functions of ${1, 1/2, \dots, 1/ n} \ {1/ i}$