3 citations · 10 across the 16 of their papers we have counts for
15 papers · 1 filter
On the Diophantine system involving pairs of triangles with the same area and the same perimeter
Yangcheng Li, Yong Zhang
Many authors studied the problem that rational triangle pairs (triangle-parallelogram pairs) with the same area and the same perimeter. They investigated this problem by solving th…
Perfect numbers and Fibonacci primes (III)
Hao Zhong, Tianxin Cai
In this article, we consider the Diophantine equation with . For some , we show that except for finitely many computable solutions in the range $n…
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 -integral rhombus pairs with a common area and a common perimeter. Moreover, we prove that there do…
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 with nonzero integers $a\eq…
On the Diophantine equations 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 for some simple…
Integers representable as the product of the sum of four integers with the sum of their reciprocals
Yong Zhang
By the theory of elliptic curves, we study the integers representable as the product of the sum of four integers with the sum of their reciprocals and give a sufficient condition f…
On the Diophantine equations involving 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 for some simple…
On the Diophantine equation involving Laurent polynomials
Yong Zhang
By the theory of elliptic curves, we investigate the nontrivial rational parametric solutions of the Diophantine equation , where and are some simpl…
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.
On the reducibility of some special quadrinomials
Yong Zhang, Huilin Zhu
Let be positive integers and let be nonzero rational numbers. We consider the reducibility of some special quadrinomials with and 5, which r…
Perfect Numbers and Fibonacci Primes (II)
Tianxin Cai, Liuquan Wang, Yong Zhang
In this paper, we study the diophantine equation . We prove that except for finitely many computable solutions, all the solutions to this equation with…
Figurate primes and Hilbert's 8th problem
Tianxin Cai, Yong Zhang, Zhongyan Shen
In this paper, by using the theory of elliptic curves, we discuss several Diophantine equations related with the so-called figurate primes. Meanwhile, we raise several conjectures…
Perfect numbers and Fibonacci primes
Tianxin Cai, Deyi Chen, Yong Zhang
In this paper, we introduce the concept of -perfect number, which is a positive integer such that . We prove that all the -perfect numbers are of th…
A New Generalization of Fermat's Last Theorem
Tianxin Cai, Deyi Chen, Yong Zhang
In this paper, we consider some hybrid Diophantine equations of addition and multiplication. We first improve a result on new Hilbert-Waring problem. Then we consider the equation…
A variety of Euler's conjecture
Tianxin Cai, Yong Zhang
We consider a variety of Euler's conjecture, i.e., whether the Diophantine system \[\begin{cases} n=a_{1}+a_{2}+\cdots+a_{s-1}, a_{1}a_{2}\cdots a_{s-1}(a_{1}+a_{2}+\cdots+a_{s-1})…