Pingzhi Yuan

collaborators

5 papers

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. Erdős 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 $φ (m^{2}) / (φ (n^{2}))^{b}$ and $φ(k(m^{2…

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…

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

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

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