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Polynomial
values in Fibonacci sequences
Adi Ostrov, Danny Neftin, Avi Berman and Reyad A. Elrazik |
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Vol. 13 (2020), No. 4, 597–605
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Abstract |
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The only perfect powers in the Fibonacci sequence are 0, 1, 8, and 144, and in the Lucas sequence, the only perfect powers are 1 and 4. We prove that in sequences that follow the same recurrence relation of the Lucas and Fibonacci sequences, there are always only finitely many polynomial values for any polynomial which is not equivalent to a Dickson polynomial. |
Keywords
recurrence sequence, polynomial values, Fibonacci
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Mathematical Subject Classification 2010
Primary: 11B39, 11C08
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Milestones
Received: 14 December 2019
Revised: 21 April 2020
Accepted: 26 July 2020
Published: 20 November 2020
Communicated by Kenneth S. Berenhaut
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Authors |
| Adi Ostrov | |
| Department of Mathematics Technion – Israel Institute of Technology Haifa Israel |
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| Danny Neftin | |
| Department of Mathematics Technion – Israel Institute of Technology Haifa Israel |
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| Avi Berman | |
| Department of Mathematics Technion – Israel Institute of Technology Haifa Israel |
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| Reyad A. Elrazik | |
| Department of Mathematics Technion – Israel Institute of Technology Haifa Israel |
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| © 2020 MSP (Mathematical Sciences Publishers). |
