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 ).

引用

页码：316 / 328

页数：13

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