Glasnik Matematicki, Vol. 55, No. 1 (2020), 13-27.

DIOPHANTINE EQUATIONS CONNECTED TO THE KOMORNIK POLYNOMIALS

András Bazsó, Attila Bérczes, Ondřej Kolouch, István Pink and Jan Šustek

Institute of Mathematics, MTA-DE Research Group ``Equations Functions and Curves'', Hungarian Academy of Sciences and University of Debrecen, P.O. Box 400, H-4002 Debrecen, Hungary
e-mail: bazsoa@science.unideb.hu

Institute of Mathematics, University of Debrecen, P.O. Box 400, H-4002 Debrecen, Hungary
e-mail: berczesa@science.unideb.hu

Department of Mathematics, University of Ostrava, 30. dubna 22, Ostrava, 701 03, Czech Republic
e-mail: ondrej.kolouch@osu.cz

Institute of Mathematics, University of Debrecen, P.O. Box 400, H-4002 Debrecen, Hungary
e-mail: pinki@science.unideb.hu

Department of Mathematics, University of Ostrava, 30. dubna 22, Ostrava, 701 03, Czech Republic
e-mail: jan.sustek@osu.cz

Abstract.   We investigate the power and polynomial values of the polynomials Pn(X) = ∏nk=0 (X2 · 3k - X3k - 1 ) for n ∈ ℕ. We prove various ineffective and effective finiteness results. In the case 0≤ n ≤ 3, we determine all pairs x,y of integers such that Pn(x)=y2 or Pn(x)=y3.

2010 Mathematics Subject Classification.   11D41, 11B83

Key words and phrases.   Diophantine equations, decomposition, polynomial values

Full text (PDF) (access from subscribing institutions only)

https://doi.org/10.3336/gm.55.1.02

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