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On the extendibility of $D(4)$-pair of Pell numbers | ||
| Journal of Algebra and Related Topics | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 06 دی 1404 | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22124/jart.2025.29584.1764 | ||
| نویسندگان | ||
| K. Moussaoui* 1؛ D. Emanuel2؛ O. Kihel2؛ A. Zekiri3 | ||
| 1Department of Algebra and Number Theory, University of Sciences and Technology Houari Boumediene, Bab Ezzouar Algiers, Algeria | ||
| 2Department of Mathematics and Statistics, Brock University, L2S 3A1, Saint Catharines Ontario, Canada | ||
| 3Department of Algebra and Number Theory, University of Sciences and Technology Houari Boumediene, Bab Ezzouar Algiers, Algeria | ||
| چکیده | ||
| Let $\ell$ be a non-zero integer, a set of $m$ distinct positive integers $\left\{a_{1},a_{2},\ldots,a_{m}\right\}$ is called a $D(\ell)$-Diophantine $m$-tuple, if $a_{i}a_{j}+\ell$ is a perfect square for any distinct $i,j\in\left\{1,2,...,m\right\}$. Let $P_n$ denote the $n^{th}$ Pell number, defined by the recurrence relation $P_{n+1}=2P_{n}+P_{n-1}$, with initial conditions $P_{0}=0$ and $P_{1}=1$. This paper investigates the extendibility of the pair $P_{2n+4}$, $4P_{2n+2}$ to a D(4)-Diophantine triple by another Pell number. | ||
| کلیدواژهها | ||
| Linear forms in logarithms؛ Diophantine triples؛ Pellian equations | ||
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آمار تعداد مشاهده مقاله: 3 |
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