Hongjian Li

collaborators

7 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 $n$ . We prove that if $(n, 6) = 1$ , then every minimal zero-sum sequence of length four over $C_{n}$ has index one, thereby resolving the length-fou…

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

Fermat's and Catalan's equations over $M_{2} (Z)$

Hongjian Li, Pingzhi Yuan

Let $A = (a c b d) \in M_{2} (Z)$ be a given matrix such that $b c \neq = 0$ and let $C (A) = {B \in M_{2} (Z) : A B = B A}$ . In this pap…

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…

A Multiplicative Fourier Proof of the Length-Four Index Conjecture

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

Fermat's and Catalan's equations over M2​(Z)

Faithful Decomposition of Rationals

Some permutation polynomials via linear translators

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

Fermat's and Catalan's equations over $M_{2} (Z)$

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