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https://hdl.handle.net/20.500.13091/4586
Title: | The K-Generalized Lucas Numbers Close to a Power of 2 | Authors: | Açıkel, Abdullah Irmak, Nurettin Szalay, Laszlo |
Keywords: | k-generalized Lucas sequence Baker method LLL reduction |
Publisher: | Walter De Gruyter Gmbh | Abstract: | Let k >= 2 be a fixed integer. The k-generalized Lucas sequence {L-n((k))}(n)>=(0) starts with the positive integer initial values k, 1, 3, ..., 2(k-1)-1, and each term afterward is the sum of the k consecutive preceding elements. An integer n is said to be close to a positive integer m if n satisfies |n-m| < root m. In this paper, we combine these two concepts. We solve completely the diophantine inequality |L-n((k)) - 2(m) | < 2(m/2) in the non-negative integers k, n, and m. This problem is equivalent to the resolution of the equation L-n((k)) = 2(m) + t with the condition |t| < 2(m/2), t is an element of Z. We also discovered a new formula for L-n((k)) which was very useful in the investigation of one particular case of the problem. | URI: | https://doi.org/10.1515/ms-2023-0064 https://hdl.handle.net/20.500.13091/4586 |
ISSN: | 0139-9918 1337-2211 |
Appears in Collections: | Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collections WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collections |
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