Skip to the main content

Original scientific paper

https://doi.org/10.3336/gm.58.1.05

Pillai's conjecture for polynomials

Sebastian Heintze ; Institute of Analysis and Number Theory, Graz University of Technology, Steyrergasse 30/II, A-8010 Graz, Austria


Full text: english pdf 374 Kb

page 67-74

downloads: 155

cite

Download JATS file


Abstract

In this paper we study the polynomial version of Pillai's conjecture on the exponential Diophantine equation
p^n - q^m = f.
We prove that for any non-constant polynomial \( f \) there are only finitely many quadruples \( (n,m,\deg p,\deg q) \) consisting of integers \( n,m \geq 2 \) and non-constant polynomials \( p,q \) such that Pillai's equation holds.
Moreover, we will give some examples that there can still be infinitely many possibilities for the polynomials \( p,q \).

Keywords

Pillai problem, polynomials, \( S \)-units

Hrčak ID:

304391

URI

https://hrcak.srce.hr/304391

Publication date:

20.6.2023.

Visits: 461 *





This display is generated from NISO JATS XML with jats-html.xsl. The XSLT engine is libxslt.