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Perfect powers from products of terms in Lucas sequences
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Bugeaud, Yann, Luca, Florian, Mignotte, Maurice and Siksek, Samir (2007) Perfect powers from products of terms in Lucas sequences. Journal fur die reine und angewandte Mathematik, Vol.611 . pp. 109-129. doi:10.1515/CRELLE.2007.075 ISSN 0075-4102.
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Official URL: http://dx.doi.org/10.1515/CRELLE.2007.075
Abstract
Suppose that {U-n}(n >= 0) is a Lucas sequence, and suppose that l(1), ..., l(t) are primes. We show that the equation
U-n1 ... U-nm =+/- l(1)(x1) ... l(t)(x1)y(p), p prime, m<p, has only finitely many solutions. Moreover, we explain a practical method of solving these equations. For example, if {F-n}(n >= 0) is the Fibonacci sequence, then we solve the equation
F-n1 ... F-nm = 2(x1). 3(x2) . 5(x3) ... 541(x100)y(p)
under the restrictions: p is prime and m < p.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Journal or Publication Title: | Journal fur die reine und angewandte Mathematik | ||||
Publisher: | Walter de Gruyter & Co | ||||
ISSN: | 0075-4102 | ||||
Official Date: | October 2007 | ||||
Dates: |
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Volume: | Vol.611 | ||||
Number of Pages: | 21 | ||||
Page Range: | pp. 109-129 | ||||
DOI: | 10.1515/CRELLE.2007.075 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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