On the Parity of the Order of Appearance in the Fibonacci Sequence

被引：2
作者：
Trojovsky, Pavel [1 ]
机构：
[1] Univ Hradec Kralove, Fac Sci, Dept Math, Hradec Kralove 50003, Czech Republic
来源：
MATHEMATICS | 2021年 / 9卷 / 16期
关键词：
order of appearance; Fibonacci numbers; parity; natural density; prime numbers; FIXED-POINTS; UPPER-BOUNDS; RANK;
D O I：
10.3390/math9161928
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let (F-n)(n >= 0) be the Fibonacci sequence. The order of appearance function (in the Fibonacci sequence) z : Z(>= 1)-> Z(>= 1) is defined as z(n) := min{k >= 1 : F-k equivalent to 0 (mod n)}. In this paper, among other things, we prove that z(n) is an even number for almost all positive integers n (i.e., the set of such n has natural density equal to 1).
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页数：8
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