Pingzhi Yuan
South China Normal University
CombinatoricsDiscrete mathematicsAlgebraAbelian groupSubsequencePermutationPrime (order theory)Pure mathematicsDiophantine equationCyclic groupZero (complex analysis)ConjecturePrime factorMathematicsSequenceDiophantine setIntegerPermutation graphCyclic permutationFinite field
112Publications
16H-index
833Citations
Publications 104
#1Hongjian Li (SCNU: South China Normal University)
#2Pingzhi Yuan (SCNU: South China Normal University)H-Index: 16
Last. Hairong Bai (SCNU: South China Normal University)
view all 3 authors...
Abstract–In this note, we show that each positive rational number can be written uniquely as φ ( m 2 ) / φ ( n 2 ) , where m , n ∈ N , with some natural restrictions on gcd ( m , n ) .
#2Pingzhi Yuan (SCNU: South China Normal University)H-Index: 16
For a prime p and positive integers m, n, let ${{\mathbb {F}}}_q be a finite field with q=p^m elements and {{\mathbb {F}}}_{q^n} be an extension of {{\mathbb {F}}}_q. Let h(x) be a polynomial over {{\mathbb {F}}}_{q^n} satisfying the following conditions: (i) {\mathrm{Tr}}_m^{nm}(x)\circ h(x)=\tau (x)\circ {\mathrm{Tr}}_m^{nm}(x) ; (ii) For any s \in {{\mathbb {F}}}_{q} , h(x) is injective on {\mathrm{Tr}}_m^{nm}(x)^{-1}(s), where \tau (x) is a polynomial over ... #1Danyao Wu (DGUT: Dongguan University of Technology)H-Index: 1 #2Pingzhi Yuan (SCNU: South China Normal University)H-Index: 16 #2Pingzhi YuanH-Index: 16 view all 3 authors... #2Pingzhi Yuan (SCNU: South China Normal University)H-Index: 16 Let s be a prime power and$ {{{\mathbb {F}}}}_q be a finite field with s elements. In this paper, we employ the AGW criterion to investigate the permutation behavior of some polynomials of the form \begin{aligned} b(x^q+ax+\delta )^{1+\frac{i(q^2-1)}{d}}+c(x^q+ax+\delta )^{1+\frac{j(q^2-1)}{d}}+L(x) \end{aligned}over {{{\mathbb {F}}}}_{q^2} with a^{1+q}=1, q\equiv \pm 1\pmod {d} and L(x)=-ax or x^q-ax. Accordingly, we also present the permutation polynomials of the form ...
#2Pingzhi YuanH-Index: 16
In 1956, Je_smanowicz conjectured that, for positive integers m and n with m > n; gcd(m; n) = 1 and m ≢ n (mod 2), the exponential Diophantine equation (m2 -n2)x + (2mn)y = (m2 + n2)z has only the positive integer solution (x; y; z) = (2; 2; 2). Recently, Ma and Chen proved the conjecture if 4 ☓mn and y ≥ 2. In this paper, we provide a proposition that, for positive integers m and n with m > n; gcd(m; n) = 1 and m2 + n2 ≡ 5 (mod 8), the exponential Diophantine equation (m2 -n2)x + (2mn)y = (m2 +...
#1Pingzhi YuanH-Index: 16
#2Kevin Zhao (SCNU: South China Normal University)H-Index: 2
Let Gbe a finite abelian group. We say that Mand Sform a \textsl{splitting} of Gif every nonzero element gof Ghas a unique representation of the form g=mswith m\in Mand s\in S while 0has no such representation. The splitting is called \textit{purely singular} if for each prime divisor pof |G| there is at least one element of Mis divisible by p In this paper, we mainly study the purely singular splittings of cyclic groups. We first prove that if k\ge3i...
#1Pingzhi Yuan (SCNU: South China Normal University)H-Index: 16
#2Kevin Zhao (SCNU: South China Normal University)H-Index: 2
Abstract Given integers k 1 , k 2 with 0 ≤ k 1 k 2 , the determination of all positive integers q for which there exists a perfect splitter B [ − k 1 , k 2 ] ( q ) set is a wide open question in general. In this paper, we obtain new necessary and sufficient conditions for an odd prime p such that there exists a nonsingular perfect B [ − 1 , 3 ] ( p ) set. We also give some necessary conditions for the existence of purely singular perfect splitter sets. In particular, we determine all perfect B [...
#1Q. Han (Guangdong University of Foreign Studies)H-Index: 1
#2Pingzhi Yuan (SCNU: South China Normal University)H-Index: 16
Jeśmanowicz [9] conjectured that, for positive integers m and n with m > n, gcd(m,n) = 1 and $${m\not\equiv n\pmod{2}}$$, the exponential Diophantine equation $${(m^2-n^2)^x+(2mn)^y=(m^2+n^2)^z}$$ has only the positive integer solution (x, y, z) = (2, 2, 2). We prove the conjecture for $${2 \| mn}$$ and m + n has a prime factor p with $${p\not\equiv1\pmod{16}}$$.
#1Pingzhi Yuan (SCNU: South China Normal University)H-Index: 16
#2Qing Han (Guangdong University of Foreign Studies)H-Index: 1
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