A class of Diophantine equations involving Bernoulli polynomials
type: Item
instance of: scholarly article
title: A class of Diophantine equations involving Bernoulli polynomials
zbMATH Open document ID: 1105.11006
DOI: 10.1016/S0019-3577(05)80014-X
author: Balasubramanian Sury
author: Manisha Kulkarni
published in: Indagationes Mathematicae. New Series
publication date: 2005-06-10T00:00:00Z
review text: Let \(a,b\in\mathbb{Q}\backslash\{0\}\) and \(C(y)\in\mathbb{Q}[(y]\). The authors consider the Diophantine equations \[ aB_m(x)=bf_n(y)+C(y) \] and \[ af_m(x)=bB_n(y)+C(y) \] with \(m\geq n>\text{deg}\;C+2\) for solutions in integers \(x,y\). Here \(f_n(y)=x(x+1)\ldots (x+n-1)\) and \(B_n(x)\) denote the Bernoulli polynomials. The main theorems give finiteness results by applying the method of \textit{Y. F. Bilu} and \textit{R. F. Tichy} [Acta Arith. 95, No.~3, 261--288 (2000; Zbl 0958.11049)].
reviewed by: Robert F. Tichy
Mathematics Subject Classification ID: 11D45
Mathematics Subject Classification ID: 11B68
zbMATH DE Number: 2175008
MaRDI profile type: Publication
cites work: Q4533267
cites work: The Diophantine equation x(x+1)...(x+(m-1)) + r= yn
cites work: The Diophantine equation f(x) = g(y)
cites work: On the Diophantine equation \(x(x + 1)(x + 2)\dots (x + (m - 1)) =g(y)\)
cites work: Diophantine equations with Bernoulli polynomials
description: scientific article; zbMATH DE number 2175008