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ON PERFECT POWERS IN LUCAS SEQUENCES
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Bugeaud, Yann, Luca, Florian, Mignotte, Maurice and Siksek, Samir (2005) ON PERFECT POWERS IN LUCAS SEQUENCES. INTERNATIONAL JOURNAL OF NUMBER THEORY, 1 (3). pp. 309-332. doi:10.1142/S1793042105000236
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Official URL: http://dx.doi.org/10.1142/S1793042105000236
Abstract
Let (u(n))(n >= 0) be the binary recurrence sequence of integers given by u(0) = 0, u(1) = 1 and u(n+2) = 2(u(n+1) + u(n)). We show that the only positive perfect powers in this sequence are u(1) = 1 and u(4) = 16. We further discuss the problem of determining perfect powers in Lucas sequences in general.
| Item Type: | Journal Article | ||||
|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||
| Journal or Publication Title: | INTERNATIONAL JOURNAL OF NUMBER THEORY | ||||
| Publisher: | WORLD SCIENTIFIC PUBL CO PTE LTD | ||||
| ISSN: | 1793-0421 | ||||
| Official Date: | September 2005 | ||||
| Dates: |
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| Volume: | 1 | ||||
| Number: | 3 | ||||
| Number of Pages: | 24 | ||||
| Page Range: | pp. 309-332 | ||||
| DOI: | 10.1142/S1793042105000236 | ||||
| Publication Status: | Published | ||||
| Funder: | France-Mexico ANUIES-ECOS | ||||
| Grant number: | M01-M02 |
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