Diophantine equations with truncated binomial polynomials
type: Item
instance of: scholarly article
title: Diophantine equations with truncated binomial polynomials
zbMATH Open document ID: 1339.11044
author: Dijana Kreso
author: A. Dubickas
published in: Indagationes Mathematicae. New Series
publication date: 2016-01-12T00:00:00Z
review text: The authors consider the Diophantine equation \(P_{n,k}(x)=P_{m,\ell}(y)\) in integers \(x,y\), where, for positive integers \(k\leq n\), \(P_{n,k}(x)=\sum_{j=0}^k {n\choose j}x^j\) is a truncated binomial expression of \((1+x)^n\). Under certain irreducibility assumptions, they show that the equation admits only finitely many solutions. There proof mainly relies on the Bilu-Tichy theorem. Further, they give some results concerning the functional decomposition of \(P_{n,k}(x)\) into two lower degree polynomials.
reviewed by: Lajos Hajdu
Mathematics Subject Classification ID: 11D41
Mathematics Subject Classification ID: 11C08
zbMATH DE Number: 6529316
zbMATH Keywords: truncated binomial expansion
zbMATH Keywords: Dickson polynomial
zbMATH Keywords: Diophantine equations
MaRDI profile type: Publication
full work available at URL: j.indag.2015.11.006
OpenAlex ID: W2185788524
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DOI: 10.1016/J.INDAG.2015.11.006
description: scientific article; zbMATH DE number 6529316