Yong Zhang

most citedHeron triangle and rhombus pairs with a common area and a common perimeter

3 citations · 5 across the 4 of their papers we have counts for

collaborators

6 papers

math.NT2017

Perfect numbers and Fibonacci primes (III)

Hao Zhong, Tianxin Cai

In this article, we consider the Diophantine equation $σ_{2} (n) - n^{2} = A n + B$ with $A = P^{2} \pm 2$ . For some $B$ , we show that except for finitely many computable solutions in the range $n…

math.NT2017★ 3 cited

Heron triangle and rhombus pairs with a common area and a common perimeter

Yong Zhang, Junyao Peng

By Fermat's method, we show that there are infinitely many Heron triangle and $θ$ -integral rhombus pairs with a common area and a common perimeter. Moreover, we prove that there do…

math.NT2017★ 2 cited

Arithmetic properties of polynomials

Yong Zhang, Zhongyan Shen

In this paper, first, we prove that the Diophantine system \[f(z)=f(x)+f(y)=f(u)-f(v)=f(p)f(q)\] has infinitely many integer solutions for $f (X) = X (X + a)$ with nonzero integers $a\eq…

math.NT2017

On the Diophantine equations $z^{2} = f (x)^{2} \pm g (y)^{2}$ concerning Laurent polynomials

Yong Zhang, Arman Shamsi Zargar

By the theory of elliptic curves, we study the nontrivial rational parametric solutions and rational solutions of the Diophantine equations $z^{2} = f (x)^{2} \pm g (y)^{2}$ for some simple…

math.NT2016

Congruent numbers on the right trapezoid

Tianxin Cai, Yong Zhang

We introduce and study a new kind of congruent number problem on the right trapezoid.

math.NT2016

On the reducibility of some special quadrinomials

Yong Zhang, Huilin Zhu

Let $n > m > k$ be positive integers and let $a, b, c$ be nonzero rational numbers. We consider the reducibility of some special quadrinomials $x^{n} + a x^{m} + b x^{k} + c$ with $n = 4$ and 5, which r…