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

共 50 条

[21] Special linearly unrelated sequences
Hancl, Jaroslav
Sobkova, Simona
JOURNAL OF MATHEMATICS OF KYOTO UNIVERSITY, 2006, 46 (01): : 31 - 45
[22] BIALGEBRAS OF LINEARLY RECURSIVE SEQUENCES
CHIN, W
GOLDMAN, J
COMMUNICATIONS IN ALGEBRA, 1993, 21 (11) : 3935 - 3952
[23] SOME PROPERTIES OF THE UNCERTAINTY FUNCTION OF FREQUENCY SEQUENCES CONSTRUCTED ON THE BASIS OF LINEAR RECURRENT SEQUENCES
GONTARENKO, VP
STRUCHEV, VF
CHEKUROV, GI
TELECOMMUNICATIONS AND RADIO ENGINEERING, 1981, 35-6 (05) : 68 - 73
[24] Generalized Euler Sequences Revisited
de Ruiter, Anton H. J.
Forbes, James Richard
JOURNAL OF THE ASTRONAUTICAL SCIENCES, 2015, 62 (01): : 1 - 20
[25] Generalized Euler Sequences Revisited
Anton H. J. de Ruiter
James Richard Forbes
The Journal of the Astronautical Sciences, 2015, 62 : 1 - 20
[26] The cross-correlation function of complications of linear recurrent sequences
Bugrov, Aleksey D.
DISCRETE MATHEMATICS AND APPLICATIONS, 2018, 28 (02): : 65 - 73
[27] Quantum convolution of linearly recursive sequences
Ng, SH
Taft, EJ
JOURNAL OF ALGEBRA, 1997, 198 (01) : 101 - 119
[28] LINEARLY RECURSIVE SEQUENCES AND OPERATOR POLYNOMIALS
GRUNENFELDER, L
OMLADIC, M
LINEAR ALGEBRA AND ITS APPLICATIONS, 1993, 182 : 127 - 145
[29] DIVIDED DIFFERENCES AND LINEARLY RECURSIVE SEQUENCES
VERDESTAR, L
STUDIES IN APPLIED MATHEMATICS, 1995, 95 (04) : 433 - 456
[30] Linearly implicit peer methods for the compressible Euler equations
Jebens, Stefan
Knoth, Oswald
Weiner, Ruediger
APPLIED NUMERICAL MATHEMATICS, 2012, 62 (10) : 1380 - 1392

← 1 2 3 4 5 →