Result: A class of Diophantine equations involving Bernoulli polynomials
Title:
A class of Diophantine equations involving Bernoulli polynomials
Authors:
Source:
Indagationes Mathematicae. 16:51-65
Publisher Information:
Elsevier BV, 2005.
Publication Year:
2005
Subject Terms:
Document Type:
Academic journal
Article
File Description:
application/xml
Language:
English
ISSN:
0019-3577
DOI:
10.1016/s0019-3577(05)80014-x
Access URL:
https://zbmath.org/2175008
https://doi.org/10.1016/s0019-3577(05)80014-x
https://www.sciencedirect.com/science/article/pii/S001935770580014X
https://dialnet.unirioja.es/servlet/articulo?codigo=1142956
https://www.isibang.ac.in/~sury/indagbern.pdf
http://www.isibang.ac.in/~sury/indagbern.pdf
https://documat.unirioja.es/servlet/articulo?codigo=1142956
https://www.sciencedirect.com/science/article/abs/pii/S001935770580014X
https://doi.org/10.1016/s0019-3577(05)80014-x
https://www.sciencedirect.com/science/article/pii/S001935770580014X
https://dialnet.unirioja.es/servlet/articulo?codigo=1142956
https://www.isibang.ac.in/~sury/indagbern.pdf
http://www.isibang.ac.in/~sury/indagbern.pdf
https://documat.unirioja.es/servlet/articulo?codigo=1142956
https://www.sciencedirect.com/science/article/abs/pii/S001935770580014X
Rights:
Elsevier Non-Commercial
Accession Number:
edsair.doi.dedup.....5daafcdddbd0c3ca2bcc6395d358021e
Database:
OpenAIRE
Further Information
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)].