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On the solutions of a system of two Diophantine equations

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Science China Mathematics 2014年第7期57卷 1401-1418页

作者： LUO JiaGui yuan pingzhi School of Mathematics and Information China West Normal University School of Mathematics and Information Sciences Zhaoqing University School of Mathematics South China Normal University

We obtain all positive integer solutions（m1,m2,a,b） with a ＆gt; b,gcd（a,b） = 1 to the system of Diophantine equations km21- lat1bt2a2r= C1,km22- lat1bt2b2r= C2,with C1,C2 ∈ {-1,1,-2,2,-4,4},and k,l,t1,t2,r ∈ Z ... 详细信息

关键词： minimal solution fundamental solution Jacobi symbol Diophantine equation

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Some New Results on Purely Singular Splittings

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Communications in Mathematical Research 2022年第2期38卷 136-156页

作者： pingzhi yuan School of Mathematical Science South China Normal UniversityGuangzhou 510631China

Let G be a finite abelian group,M a set of integers and S a subset of *** say that M and S form a splitting of G if every nonzero element g of G has a unique representation of the form g=m s with m∈M and s∈S,while 0 has no such *** splitting is called purely singular if for each prime divisor p of|G|,there is at least one element of M is divisible by *** this paper,we continue the study of purely singular splittings of cyclic *** prove that if k≥2 is a positive integer such that[−2 k+1,2 k+2]^(∗)splits a cyclic group Z m,then m=4 k+*** prove also that if M=[−k_(1),k_(2)]^(∗)splits Z m purely singularly,and 15≤k_(1)+k_(2)≤30,then m=1,or m=k_(1)+k_(2)+1,or k_(1)=0 and m=2 k_(2)+1.

关键词： Splitter sets perfect codes factorizations of cyclic groups

A parametric family of quartic Thue equations

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Frontiers of Mathematics in China 2023年第3期18卷 147-163页

作者： Zhigang LI pingzhi yuan School of Mathematics and Computing Science Hunan University of Science and TechnologyXiangtan 411201China School of Mathematics South China Normal UniversityGuangzhou 510631China

In this paper,we give all primitive solutions of a parameterized family of quartic Thue equations:x^(4)-4cx^(3)y+(6c+2)x^(2)y^(2)+4cxy^(3)+y^(4)=96c+169,c>0.

关键词： Extension of classical Legendre's theorem Baker-Wistholz's theo-rem Thue equation

Permutation Polynomials of ■

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Journal of Mathematical Research with Applications 2023年第2期43卷 166-174页

作者： Danyao WU pingzhi yuan School of Computer Science and Technology Dongguan University of Technology School of Mathematics South China Normal University

Let m be a positive integer and Fqr be a finite field with the characteristic of p. We prove that if p > m2-m and q ≡ 1(mod m), the polynomial x(1+(q-1)/m) + ax(a =≠ 0) is not a permutation polynomial over Fqr(r ≥ 2). And we verify that if q ≡ 1(mod 7) and p≠ 2, 3,then the polynomial x(1+(q-1)/7) + ax(a =≠ 0) is not a permutation polynomial over Fqr(r ≥ 2).

关键词： polynomial permutation polynomial finite field

More Divisibility Properties for Binomial Coefficients

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Journal of Mathematical Research with Applications 2022年第6期42卷 561-579页

作者： Jiaqi XIAO Yuqing HE pingzhi yuan School of Mathematics South China Normal University

Let a, b and n be positive integers with a > b, we prove the following divisibility property: For all positive integers n, we have ■which extends the result of Yang. And for all positive integers n, we show the follo... 详细信息

关键词： binomial coefficients p-adic order divisibility property

Symmetric Digraphs from Powers Modulo <i>n</i>

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Open Journal of Discrete Mathematics 2011年第3期1卷 103-107页

作者： Guixin Deng pingzhi yuan School of Mathematics Guangxi Teachers Education University School of Mathematics South China Normal University

For each pair of positive integers n and k, let G(n,k) denote the digraph whose set of vertices is H = {0,1,2,···, n – 1} and there is a directed edge from a ∈ H to b ∈ H if a ≡ b(mod n). The digraph G(n,k) is symmetric if its connected component can be partitioned into isomorphic pairs. In this paper we obtain all symmetric G(n,k)

关键词： Congruence Digraph Component Height Cycle

On the diophantine equation X^2-(1+a^2)Y^4 =-2a

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Science China Mathematics 2010年第8期53卷 2143-2158页

作者： yuan pingzhi 1 & ZHANG ZhongFeng 2 1 School of Mathematics,South China Normal University,Guangzhou 510631,China 2 School of Mathematics & Computational Science,Sun Yat-Sen University,Guangzhou 510275,China 1. School of Mathematics South China Normal University Guangzhou 510631 China2. School of Mathematics & Computational Science Sun Yat-Sen University Guangzhou 510275 China

Let a≥1 be an *** this paper,we will prove the equation in the title has at most three positive integer solutions.

关键词： algebraic approximations continued fractions elliptic curves quartic equations

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