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On solutions of the Diophantine equation $F_{n_{1}}+F_{n_{2}}+F_{n_{3}}+F_{n_{4}}=2^a$ | ||
| Journal of Algebra and Related Topics | ||
| دوره 9، شماره 2، اسفند 2021، صفحه 131-148 اصل مقاله (368.17 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22124/jart.2021.19294.1266 | ||
| نویسندگان | ||
| P. Tiebekabe* 1؛ I. Diouf2 | ||
| 1Department of Mathematics and Computer Science, University of Cheikh Anta Diop, Dakar, Senegal. | ||
| 2Department of Mathematics and Computer Science, University of Cheikh Anta Diop,, Dakar, Senegal. | ||
| چکیده | ||
| Let $(F_n)_{n\geq 0}$ be the Fibonacci sequence given by $F_0 = 0, F_1 = 1$ and $F_{n+2} = F_{n+1}+F_n$ for $n \geq 0$. In this paper, we solve all powers of two which are sums of four Fibonacci numbers with a few exceptions that we characterize. | ||
| کلیدواژهها | ||
| Linear forms in logarithm؛ Diophantine equations؛ Fibonacci sequence؛ Lucas sequence؛ perfect powers | ||
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آمار تعداد مشاهده مقاله: 837 تعداد دریافت فایل اصل مقاله: 869 |
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