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

[1] On the Diophantine equation yp=f(x)g(x)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${y^{p} = \frac{f(x)}{g(x)}}$$\end{document}
S. Subburam
A. Togbé
Acta Mathematica Hungarica, 2019, 157 (1) : 1 - 9
[2] On b\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ b$$\end{document}-concatenations of two k\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ k$$\end{document}-generalized Fibonacci numbers
M. Alan
A. Altassan
Acta Mathematica Hungarica, 2025, 175 (2) : 452 - 471
[3] On the diophantine equation y2=∏i≤8(x+ki)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varvec{y^{2} = \prod _{i \le 8}(x + k_i)}$$\end{document}
R Srikanth
S Subburam
Proceedings - Mathematical Sciences, 2018, 128 (4)
[4] The diophantine equation (y+q1)(y+q2)⋯(y+qm)=f(x)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${(y + q_{1})(y + q_{2})\cdots(y + q_{m}) = f(x)}$$\end{document}
S. Subburam
Acta Mathematica Hungarica, 2015, 146 (1) : 40 - 46
[5] A note on the Diophantine equation f(x)f(y)=f(z2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f(x)f(y)=f(z^2)$$\end{document}
Yong Zhang
Tianxin Cai
Periodica Mathematica Hungarica, 2015, 70 (2) : 209 - 215
[6] On the Diophantine equation x2+C=yn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x^2+C=y^n$$\end{document}
Sai Gopal Rayaguru
Indian Journal of Pure and Applied Mathematics, 2024, 55 (1) : 69 - 77
[7] A Pellian Equation with Primes and Applications to D(-1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$D(-1)$$\end{document}-Quadruples
Andrej Dujella
Mirela Jukić Bokun
Ivan Soldo
Bulletin of the Malaysian Mathematical Sciences Society, 2019, 42 (5) : 2915 - 2926
[8] On solutions of the diophantine equation Fn-Fm=3a\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varvec{F_{n}-F_{m}=3^{a}}$$\end{document}
Bahar Demirtürk Bitim
Refik Keskin
Proceedings - Mathematical Sciences, 2019, 129 (5)
[9] On the Diophantine equation x2+bm=cn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varvec{x^2+b^m=c^n}$$\end{document} with a2+b4=c2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varvec{a^2+b^4=c^2}$$\end{document}
Nobuhiro Terai
Indian Journal of Pure and Applied Mathematics, 2022, 53 (1) : 162 - 169
[10] On the variant Qn!=Px\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Q\left(n!\right)=P\left(x\right)$$\end{document} of the Brocard–Ramanujan Diophantine equation
Abderrahim Makki Naciri
The Ramanujan Journal, 2024, 65 (4) : 1791 - 1798

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