Publication date: 30 June 2023
Volume: Vol 58
Issue: Svezak 1
Pages: 67-74
DOI: 10.3336/gm.58.1.05
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
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 \( p,q \).
Pillai problem, polynomials, \( S \)-units
304391
20.6.2023.
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