Zobrazeno 1 - 10
of 273
pro vyhledávání: '"Yuan, Pingzhi"'
The definition of many-to-one mapping, or $m$-to-$1$ mapping for short, between two finite sets is introduced in this paper, which unifies and generalizes the definitions of $2$-to-$1$ mappings and $n$-to-$1$ mappings. A generalized local criterion i
Externí odkaz:
http://arxiv.org/abs/2408.04218
Autor:
Li, Hongjian, Yuan, Pingzhi
Let $\mathbb{N}$ be the set of all positive integers and let $a,\, b,\, c$ be nonzero integers such that $\gcd\left(a,\, b,\, c\right)=1$. In this paper, we prove the following three results: (1) the solvability of the matrix equation $aX^m+bY^n=cI,\
Externí odkaz:
http://arxiv.org/abs/2212.14139
Let $k, l, a$ and $b$ be positive integers with $\max\{a, \, b\}\ge2$. In this paper, we show that every positive rational number can be written as the form $\varphi(km^{a})/\varphi(ln^{b})$, where $m, \, n\in\mathbb{N}$ if and only if $\gcd(a, \,b)=
Externí odkaz:
http://arxiv.org/abs/2212.00918
Autor:
Yuan, Pingzhi
In this paper, we provide a local method to find compositional inverses of all PPs, some new PPs and their compositional inverses are given.
Comment: arXiv admin note: substantial text overlap with arXiv:2206.04252
Comment: arXiv admin note: substantial text overlap with arXiv:2206.04252
Externí odkaz:
http://arxiv.org/abs/2211.10083
In the present paper we introduce old and new results related to St\"ormer theorem about Pell equations. Moreover we give four types of applications of these results.
Externí odkaz:
http://arxiv.org/abs/2210.12576
Publikováno v:
Finite Fields Appl. 46 (2017)
Permutation polynomials are an interesting subject of mathematics and have applications in other areas of mathematics and engineering. In this paper, we determine all permutation trinomials over $\mathbb{F}_{2^m}$ in Zieve's paper. We prove a conject
Externí odkaz:
http://arxiv.org/abs/2209.04762
Autor:
Yuan, Pingzhi
In this paper, we prove that every PP is an AGW-PP. We also extend the result of Wan and Lidl to other permutation polynomials over finite fields and determine their group structure. Moreover, we provide a new general method to find the compositional
Externí odkaz:
http://arxiv.org/abs/2206.04252
Autor:
Yuan, Pingzhi
In this paper, we present two methods to obtain the compositional inverses of AGW-PPs. We improve some known results in this topic.
Comment: arXiv admin note: text overlap with arXiv:2004.12552 by other authors
Comment: arXiv admin note: text overlap with arXiv:2004.12552 by other authors
Externí odkaz:
http://arxiv.org/abs/2203.00279
Publikováno v:
Bulletin Math\'{e} matique de la Soci\'{e} t\'{e} des Sciences Math\'{e} matiques de Roumanie (2021)
In 2012, T. Miyazaki and A. Togb\'{e} gave all of the solutions of the Diophantine equations $(2am-1)^x+(2m)^y=(2am+1)^z$ and $b^x+2^y=(b+2)^z$ in positive integers $x,y,z,$ $a>1$ and $b\ge 5$ odd. In this paper, we propose a similar problem (which w
Externí odkaz:
http://arxiv.org/abs/2105.10364
Autor:
Wu, Danyao, Yuan, Pingzhi
Publikováno v:
In Finite Fields and Their Applications January 2024 93