A Diophantine equation with the harmonic mean

被引：1

作者：

Zhang, Yong ^{[1
,2
]}

Chen, Deyi ^{[3
]}

机构：

[1] Changsha Univ Sci & Technol, Sch Math & Stat, Changsha, Hunan, Peoples R China

[2] Hunan Prov Key Lab Math Modeling & Anal Engn, Changsha 410114, Hunan, Peoples R China

[3] Zhejiang Univ, Sch Math Sci, Hangzhou 310027, Zhejiang, Peoples R China

来源：

PERIODICA MATHEMATICA HUNGARICA | 2020年 / 80卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Diophantine equation; Pell's equation; Integer solutions; Rational parametric solutions; F(X)F(Y);

D O I：

10.1007/s10998-019-00302-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let f is an element of Q[x] be a polynomial without multiple roots and degf >= 2. We give conditions for f=x2+bx+cunder which the Diophantine equation 2f(x)f(y)=f(z)(f(x)+f(y))\ has infinitely many nontrivial integer solutions and prove that this equation has infinitely many rational parametric solutions for f=x2+bx with nonzero integer b. Moreover, we show that it has a rational parametric solution for infinitely many cubic polynomials.

引用

页码：138 / 144

页数：7

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