On Diophantine equations involving Lucas sequences
In this paper, we shall study the Diophantine equation un = R(m)P(m)Q(m), where un is a Lucas sequence and R, P and Q are polynomials (under weak assumptions).
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2019-08-01
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| Series: | Open Mathematics |
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| Online Access: | https://doi.org/10.1515/math-2019-0073 |
| _version_ | 1818596021307965440 |
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| author | Trojovský Pavel |
| author_facet | Trojovský Pavel |
| author_sort | Trojovský Pavel |
| collection | DOAJ |
| description | In this paper, we shall study the Diophantine equation un = R(m)P(m)Q(m), where un is a Lucas sequence and R, P and Q are polynomials (under weak assumptions). |
| first_indexed | 2024-12-16T11:25:17Z |
| format | Article |
| id | doaj.art-e28ad6b3a2174872a0079069e55fec45 |
| institution | Directory Open Access Journal |
| issn | 2391-5455 |
| language | English |
| last_indexed | 2024-12-16T11:25:17Z |
| publishDate | 2019-08-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Open Mathematics |
| spelling | doaj.art-e28ad6b3a2174872a0079069e55fec452022-12-21T22:33:23ZengDe GruyterOpen Mathematics2391-54552019-08-0117194294610.1515/math-2019-0073math-2019-0073On Diophantine equations involving Lucas sequencesTrojovský Pavel0Department of Mathematics, Faculty of Science, University of Hradec Králové, Rokitanského 62, Hradec Králové, 50003,Czech RepublicIn this paper, we shall study the Diophantine equation un = R(m)P(m)Q(m), where un is a Lucas sequence and R, P and Q are polynomials (under weak assumptions).https://doi.org/10.1515/math-2019-0073p-adic orderfibonacci numberlucas sequenceorder of appearancetridiagonal matrix11b3711b39 |
| spellingShingle | Trojovský Pavel On Diophantine equations involving Lucas sequences Open Mathematics p-adic order fibonacci number lucas sequence order of appearance tridiagonal matrix 11b37 11b39 |
| title | On Diophantine equations involving Lucas sequences |
| title_full | On Diophantine equations involving Lucas sequences |
| title_fullStr | On Diophantine equations involving Lucas sequences |
| title_full_unstemmed | On Diophantine equations involving Lucas sequences |
| title_short | On Diophantine equations involving Lucas sequences |
| title_sort | on diophantine equations involving lucas sequences |
| topic | p-adic order fibonacci number lucas sequence order of appearance tridiagonal matrix 11b37 11b39 |
| url | https://doi.org/10.1515/math-2019-0073 |
| work_keys_str_mv | AT trojovskypavel ondiophantineequationsinvolvinglucassequences |