ON THE EULER FUNCTION OF LINEARLY RECURRENT SEQUENCES

被引：0
|
作者：
Luca, Florian [1 ]
Manape, Makoko campbell [2 ]
机构：
[1] Stellenbosch Univ, Math Div, Stellenbosch, South Africa
[2] Univ Witwatersrand, Sch Math, Johannesburg, South Africa
来源：
FIBONACCI QUARTERLY | 2024年 / 62卷 / 04期
关键词：
ARITHMETIC FUNCTIONS; FIBONACCI;
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we show that if (U-n)(n >= 1) is any nondegenerate linearly recurrent sequence of integers whose general term is up to sign not a polynomial in n, then the inequality phi (|U-n|) >= |U-phi(n)|holds on a set of positive integers n of density 1, where phi is the Euler function.We show that the set of n <= x for which the above inequality fails has counting function O-U(x/log x ).
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收藏
页码：316 / 328
页数：13
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