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On the diophantine equation x(2) + C=2y(n)
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Abu Muriefah, Fadwa S., Luca, Florian, Siksek, Samir and Tengely, Szabolcs (2009) On the diophantine equation x(2) + C=2y(n). International Journal of Number Theory, Vol.5 (No.6). pp. 1117-1128. doi:10.1142/S1793042109002572 ISSN 1793-0421.
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Official URL: http://dx.doi.org/10.1142/S1793042109002572
Abstract
In this paper, we study the Diophantine equation x(2) + C = 2y(n) in positive integers x, y with gcd(x, y) = 1, where n >= 3 and C is a positive integer. If C = 1 (mod 4), we give a very sharp bound for prime values of the exponent n; our main tool here is the result on existence of primitive divisors in Lehmer sequences due to Bilu, Hanrot and Voutier. We illustrate our approach by solving completely the equations x(2) + 17(a1) = 2y(n), x(2) + 5(a1)13(a2) = 2y(n) and x(2) + 3(a1)11(a2) = 2y(n).
| Item Type: | Journal Article | ||||
|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
| Journal or Publication Title: | International Journal of Number Theory | ||||
| Publisher: | World Scientific Publishing Co. Pte. Ltd. | ||||
| ISSN: | 1793-0421 | ||||
| Official Date: | September 2009 | ||||
| Dates: |
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| Volume: | Vol.5 | ||||
| Number: | No.6 | ||||
| Number of Pages: | 12 | ||||
| Page Range: | pp. 1117-1128 | ||||
| DOI: | 10.1142/S1793042109002572 | ||||
| Status: | Peer Reviewed | ||||
| Publication Status: | Published | ||||
| Access rights to Published version: | Restricted or Subscription Access | ||||
| Funder: | CONACyT, Engineering and Physical Sciences Research Council (EPSRC), MarieCurie International Reintegration | ||||
| Grant number: | 46755, MIRG-CT-2006-044530 |
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