P. Yuan

activity

20092025

F_{2^{m}}

: a corrected version

64 citations · 114 across the 30 of their papers we have counts for

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17 papers · 1 filter

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.NT2022

The matrix equation $a X^{m} + b Y^{n} = c I$ over $M_{2} (Z)$

Hongjian Li, Pingzhi Yuan

Let $N$ be the set of all positive integers and let $a, b, c$ be nonzero integers such that $g cd (a, b, c) = 1$ . In this paper, we prove the following thr…

math.NT2022

Positive rational number of the form $φ (k m^{a}) / φ (l n^{b})$

Hongjian Li, Pingzhi Yuan, Hairong Bai

Let $k, l, a$ and $b$ be positive integers with $max {a, b} \geq 2$ . In this paper, we show that every positive rational number can be written as the form $φ (k m^{a}) / φ (l n^{b})$ ,…

math.NT2022★ 1 cited

Local Method for Compositional Inverses of Permutational Polynomials

Pingzhi Yuan

In this paper, we provide a local method to find compositional inverses of all PPs, some new PPs and their compositional inverses are given.

math.NT2022

On The St $o ¨$ rmer Theorem And Its Applications

Pingzhi Yuan, Jiagui Luo, Alain Togbé

In the present paper we introduce old and new results related to Störmer theorem about Pell equations. Moreover we give four types of applications of these results.

math.NT2021

The Shuffle Variant of a Diophantine equation of Miyazaki and Togbé

Elif Kızıldere, Gökhan Soydan, Qing Han +1

In 2012, T. Miyazaki and A. Togbé gave all of the solutions of the Diophantine equations $(2 am - 1)^{x} + (2 m)^{y} = (2 am + 1)^{z}$ and $b^{x} + 2^{y} = (b + 2)^{z}$ in positive integers $x, y, z,$ $a > 1$ and…

math.NT2020

On the exponential Diophantine equation $(n - 1)^{x} + (n + 2)^{y} = n^{z}$

Hairong Bai, Elif Kızıldere, Gökhan Soydan +1

Suppose that $n$ is a positive integer. In this paper, we show that the exponential Diophantine equation $(n - 1)^{x} + (n + 2)^{y} = n^{z}, n \geq 2, x y z \neq = 0$ has only the positive i…

math.NT2020

Purely singular splittings of cyclic groups

Pingzhi Yuan, Kevin Zhao

Let $G$ be a finite abelian group. We say that $M$ and $S$ form a \textsl{splitting} of $G$ if every nonzero element $g$ of $G$ has a unique representation of the form $g = m s$ with…

math.NT2019

An elementary proof of a result Ma and Chen

Qing Han, Pingzhi Yuan

In 1956, Je $s ˊ$ manowicz conjectured that, for positive integers $m$ and $n$ with $m > n, g cd (m, n) = 1$ and $m \neq \equiv n (mod 2)$ , the exponential Diophantine equation $…

math.NT2016

A characterization of arithmetic functions satisfying $f (u^{2} + k v^{2}) = f^{2} (u) + k f^{2} (v)$

Lihua You, Yafei Chen, Pingzhi Yuan

In this paper, we mainly discuss the characterization of a class of arithmetic functions $f : N \to C$ such that $f (u^{2} + k v^{2}) = f^{2} (u) + k f^{2} (v)$ $(k, u, v \in N)$ . We obt…

math.NT2015★ 20 cited

Large classes of permutation polynomials over $F_{q^{2}}$

Yanbin Zheng, Pingzhi Yuan, Dingyi Pei

Permutation polynomials (PPs) of the form $(x^{q} - x + c)^{\frac{q ^{2} - 1}{3} + 1} + x$ over $F_{q^{2}}$ were presented by Li, Helleseth and Tang [Finite Fields Appl. 22 (2013) 1…

math.NT2015★ 10 cited

On products of k atoms II

Alfred Geroldinger, David J. Grynkiewicz, Pingzhi Yuan

Let $H$ be a Krull monoid with class group $G$ such that every class contains a prime divisor (for example, rings of integers in algebraic number fields or holomorphy rings in alge…

math.NT2015

On the sum of reciprocal generalized Fibonacci numbers

Pingzhi Yuan, Zilong He, Junyi Zhuo

In this paper, we consider infinite sums derived from the reciprocals of the generalized Fibonacci numbers. We obtain some new and interesting identities for the generalized Fibona…

math.NT2009

Subsequence Sums of Zero-sum free Sequences II

Pingzhi Yuan

Let $G$ be a finite abelian group, and let $S$ be a sequence over $G$ . Let $f (S)$ denote the number of elements in $G$ which can be expressed as the sum over a nonempty subsequence…

math.NT2009

Davenport constant with weights

Pingzhi Yuan, Xiangneng Zeng

For the cyclic group $G = Z / n Z$ and any non-empty $A \in Z$ . We define the Davenport constant of $G$ with weight $A$ , denoted by $D_{A} (n)$ , to be the least na…

math.NT2009★ 2 cited

On the transcendence of some infinite sums

Pingzhi Yuan, Juan Li

In this paper we investigate the infinite convergent sum $T = \sum_{n = 0}^{\infty} \frac{P ( n )}{Q ( n )}$ , where $P (x) \in Q ˉ [x]$ , $Q (x) \in Q [x]$ and $Q (x)$ has only simp…

math.NT2009★ 1 cited

Coefficients of cyclotomic polynomials

Pingzhi Yuan

Let $a (n, k)$ be the $k$ -th coefficient of the $n$ -th cyclotomic polynomial. Recently, Ji, Li and Moree \cite{JLM09} proved that for any integer $m \geq 1$ , $\{a(mn, k)| n, k\in\mathb…

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

The matrix equation aXm+bYn=cI over M2​(Z)

Positive rational number of the form φ(kma)/φ(lnb)

Local Method for Compositional Inverses of Permutational Polynomials

On The Sto¨rmer Theorem And Its Applications

The Shuffle Variant of a Diophantine equation of Miyazaki and Togbé

On the exponential Diophantine equation (n−1)x+(n+2)y=nz

Purely singular splittings of cyclic groups

An elementary proof of a result Ma and Chen

A characterization of arithmetic functions satisfying f(u2+kv2)=f2(u)+kf2(v)

Large classes of permutation polynomials over Fq2​

On products of k atoms II

On the sum of reciprocal generalized Fibonacci numbers

Subsequence Sums of Zero-sum free Sequences II

Davenport constant with weights

On the transcendence of some infinite sums

Coefficients of cyclotomic polynomials

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

The matrix equation $a X^{m} + b Y^{n} = c I$ over $M_{2} (Z)$

Positive rational number of the form $φ (k m^{a}) / φ (l n^{b})$

On The St $o ¨$ rmer Theorem And Its Applications

On the exponential Diophantine equation $(n - 1)^{x} + (n + 2)^{y} = n^{z}$

A characterization of arithmetic functions satisfying $f (u^{2} + k v^{2}) = f^{2} (u) + k f^{2} (v)$

Large classes of permutation polynomials over $F_{q^{2}}$