Diophantine equations connected to the Komornik polynomials
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.
| Permalink: | http://skupni.nsk.hr/Record/nsk.NSK01001098349/Details |
|---|---|
| Matična publikacija: |
Glasnik matematički (Online) 55 (2020), 1 ; str. 13-27 |
| Glavni autori: | Bazsó, András (Author), Berczes, Attila, Kolouch, Ondřej, Pink, István, Šustek, Jan |
| Vrsta građe: | e-članak |
| Jezik: | eng |
| Predmet: | |
| Online pristup: |
https://doi.org/10.3336/gm.55.1.02 Hrčak |
| LEADER | 01581naa a22003854i 4500 | ||
|---|---|---|---|
| 001 | NSK01001098349 | ||
| 003 | HR-ZaNSK | ||
| 005 | 20210607133216.0 | ||
| 006 | m d | ||
| 007 | cr|||||||||||| | ||
| 008 | 210420s2020 ci d |o |0|| ||eng | ||
| 024 | 7 | |2 doi |a 10.3336/gm.55.1.02 | |
| 035 | |a (HR-ZaNSK)001098349 | ||
| 040 | |a HR-ZaNSK |b hrv |c HR-ZaNSK |e ppiak | ||
| 041 | 0 | |a eng |b eng | |
| 042 | |a croatica | ||
| 044 | |a ci |c hr | ||
| 080 | 1 | |a 51 |2 2011 | |
| 100 | 1 | |a Bazsó, András |4 aut | |
| 245 | 1 | 0 | |a Diophantine equations connected to the Komornik polynomials |h [Elektronička građa] / |c András Bazsó, Attila Bérczes, Ondřej Kolouch, István Pink, Jan Šustek. |
| 300 | |b Graf. prikazi. | ||
| 504 | |a Bibliografske bilješke na kraju teksta. | ||
| 504 | |a Summary. | ||
| 520 | |a 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. | ||
| 653 | 0 | |a Diofantske jednadžbe |a Dekompozicija |a Polinomi | |
| 700 | 1 | |a Berczes, Attila |4 aut | |
| 700 | 1 | |a Kolouch, Ondřej |4 aut |9 HR-ZaNSK | |
| 700 | 1 | |a Pink, István |4 aut | |
| 700 | 1 | |a Šustek, Jan |4 aut |9 HR-ZaNSK | |
| 773 | 0 | |t Glasnik matematički (Online) |x 1846-7989 |g 55 (2020), 1 ; str. 13-27 |w nsk.(HR-ZaNSK)000659858 | |
| 981 | |b Be2020 |b B03/20 | ||
| 998 | |b tino2106 | ||
| 856 | 4 | 0 | |u https://doi.org/10.3336/gm.55.1.02 |
| 856 | 4 | 0 | |u https://hrcak.srce.hr/239039 |y Hrčak |
| 856 | 4 | 1 | |y Digitalna.nsk.hr |