On the Diophantine equation ∏i≤m(diy+qi)=f(x)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\displaystyle \prod \nolimits _{i \le m}(d_iy + q_{i}) = f(x)$$\end{document}

被引：0

作者：

Raghavendran Srikanth

Sivanarayanapandian Subburam

机构：

[1] SASTRA Deemed to be University,TATA Realty

来源：

Afrika Matematika | 2018年 / 29卷 / 7-8期

关键词：

Diophantine equation; Monic polynomial; Arithmetical function; 11D41; 11D45;

D O I：

10.1007/s13370-018-0603-3

中图分类号：

学科分类号：

摘要：

In this paper, we extend the result of Subburam (Acta Math Hungar 146:40–46, 2015).

引用

页码：1091 / 1095

页数：4

共 32 条

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P. K. Bhoi
S. S. Rout
G. K. Panda
[J]. The Ramanujan Journal, 2025, 66 (2)
[22] The divisibility of the class number of the imaginary quadratic fields Q(1-2mk)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {Q}}(\sqrt{1-2m^k})$$\end{document}
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[J]. The Ramanujan Journal, 2024, 64 (3) : 991 - 1002
[23] On integral graphs which belong to the class\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\overline {\alpha K_{a,a} \cup \beta {\rm K}_{b,b} } $$ \end{document}
Mirko Lepović
[J]. Journal of Applied Mathematics and Computing, 2006, 20 (1-2) : 61 - 74
[24] On integral graphs which belong to the class\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\overline {\alpha K_a \cup \beta K_b } $$ \end{document}
Mirko Lepović
[J]. Journal of Applied Mathematics and Computing, 2004, 14 (1-2) : 39 - 49
[25] On the Diophantine Equation cx2+p2m=4yn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$cx^2+p^{2m}=4y^n$$\end{document}
K. Chakraborty
A. Hoque
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[J]. Results in Mathematics, 2021, 76 (2)
[26] The equation x4+2ny4=z4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x^4+2^ny^4=z^4$$\end{document} in algebraic number fields
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[J]. Acta Mathematica Hungarica, 2022, 167 (1) : 309 - 331
[27] On the Diophantine equation ∑j=1kjPjp=Pnq\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sum_{j=1}^{k}jP_j^p=P_n^q$$\end{document}
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[J]. Acta Mathematica Hungarica, 2020, 162 (2) : 647 - 676
[28] On the Diophantine equation \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $\dfrac{ax^{n+2l}+c}{abt^{2}x^{n}+c}{\displaystyle\frac{ax^{n+2l}+c}{abt^{2}x^{n}+c}}=by^{2}$ \end{document}
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Pingzhi Yuan
[J]. Acta Mathematica Hungarica, 2011, 133 (4) : 342 - 358
[29] On the Diophantine Equation dx2+p2aq2b=4yp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$dx^2+p^{2a}q^{2b}=4y^p$$\end{document}
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[J]. Results in Mathematics, 2022, 77 (1)
[30] On 1w+1x+1y+1z=12\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\frac{1}{w} + \frac{1}{x} + \frac{1}{y} + \frac{1}{z} = \frac{1}{ 2} $\end{document} and some of its generalizations
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[J]. Journal of Inequalities and Applications, 2018 (1)

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