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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

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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:
DateEvent
September 2005UNSPECIFIED
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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