Article
| Title: | Mersenne numbers as a difference of two Lucas numbers (English) |
| Author: | Alan, Murat |
| Language: | English |
| Journal: | Commentationes Mathematicae Universitatis Carolinae |
| ISSN: | 0010-2628 (print) |
| ISSN: | 1213-7243 (online) |
| Volume: | 63 |
| Issue: | 3 |
| Year: | 2022 |
| Pages: | 269-276 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | Let $(L_n)_{n\geq 0}$ be the Lucas sequence. We show that the Diophantine equation $ L_n-L_m=M_k$ has only the nonnegative integer solutions $(n,m,k)= (2,0,1)$, $(3, 1, 2)$, $(3, 2, 1)$, $(4, 3, 2)$, $(5, 3, 3)$, $(6, 2, 4)$, $(6, 5, 3)$ where $ M_k=2^k-1 $ is the $k$th Mersenne number and $ n > m$. (English) |
| Keyword: | Lucas number |
| Keyword: | Mersenne number |
| Keyword: | Diophantine equation |
| Keyword: | linear forms in logarithm |
| MSC: | 11B39 |
| MSC: | 11D61 |
| MSC: | 11J86 |
| idZBL: | Zbl 07655799 |
| idMR: | MR4542788 |
| DOI: | 10.14712/1213-7243.2022.027 |
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| Date available: | 2023-02-01T12:00:20Z |
| Last updated: | 2023-04-20 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/151474 |
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