Greatest Common Divisors in Shifted Fibonacci Sequences

被引：0
|
作者：
Chen, Kwang-Wu [1 ]
机构：
[1] Taipei Municipal Univ Educ, Dept Math & Comp Sci Educ, 1,Ai Kuo West Road, Taipei, Taiwan
来源：
JOURNAL OF INTEGER SEQUENCES | 2011年 / 14卷 / 04期
关键词：
Fibonacci numbers; Lucas numbers; generalized Fibonacci numbers;
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
It is well known that successive members of the Fibonacci sequence are relatively prime. Let f(n)(a) = gcd(F-n + a, Fn+1 + a). Therefore (f(n)(0)) is the constant sequence 1, 1, 1,..., but Hoggatt in 1971 noted that (f(n) (+/- 1)) is unbounded. In this note we prove that (f(n)(a)) is bounded if a not equal +/- 1.
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页数：8
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