The extendibility of Diophantine pairs with Fibonacci numbers and some conditions
A set $\{a_1, a_2, \cdots, a_m\}$ of positive integers is called a Diophantine $m$-tuple if $a_ia_j+1$ is a perfect square for all $1\leq i < j \leq m$. Let $F_n$ be the $n$th Fibonacci number which is defined by $F_0=0, F_1=1$ and $F_{n+2}=F_{n+1}+F_n$. In this paper, we find the extendibility o...
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| Published in | 충청수학회지, 34(3) pp. 209 - 219 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
충청수학회
01.08.2021
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| Subjects | |
| Online Access | Get full text |
| ISSN | 1226-3524 2383-6245 |
| DOI | 10.14403/jcms.2021.34.3.209 |
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| Summary: | A set $\{a_1, a_2, \cdots, a_m\}$ of positive integers is called a Diophantine $m$-tuple if $a_ia_j+1$ is a perfect square for all $1\leq i < j \leq m$. Let $F_n$ be the $n$th Fibonacci number which is defined by $F_0=0, F_1=1$ and $F_{n+2}=F_{n+1}+F_n$. In this paper, we find the extendibility of Diophantine pairs $\{F_{2k}, b\}$ with some conditions. KCI Citation Count: 0 |
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| ISSN: | 1226-3524 2383-6245 |
| DOI: | 10.14403/jcms.2021.34.3.209 |