Glasnik matematički, Vol. 55 No. 1, 2020.
Original scientific paper
https://doi.org/10.3336/gm.55.1.02
Diophantine equations connected to the Komornik polynomials
András Bazsó
orcid.org/0000-0002-9956-1152
; 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
Attila Bérczes
; Institute of Mathematics, University of Debrecen, P.O. Box 400, H-4002 Debrecen, Hungary
Ondřej Kolouch
; Department of Mathematics, University of Ostrava, 30. dubna 22, Ostrava, 701 03, Czech Republic
István Pink
; Institute of Mathematics, University of Debrecen, P.O. Box 400, H-4002 Debrecen, Hungary
Jan Šustek
; Department of Mathematics, University of Ostrava, 30. dubna 22, Ostrava, 701 03, Czech Republic
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.
Keywords
Diophantine equations; decomposition; polynomial values
Hrčak ID:
239039
URI
Publication date:
12.6.2020.
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