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

[41] On Euler's function
Liu, H. -Q.
PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2016, 146 (04) : 769 - 775
[42] On the Euler function of repdigits
Florian Luca
Czechoslovak Mathematical Journal, 2008, 58 : 51 - 59
[43] GEOMETRY AND RECURRENT SEQUENCES
DENIS, L
BULLETIN DE LA SOCIETE MATHEMATIQUE DE FRANCE, 1994, 122 (01): : 13 - 27
[44] CONDITIONAL RECURRENT SEQUENCES
SMITS, THM
INDAGATIONES MATHEMATICAE-NEW SERIES, 1991, 2 (03): : 359 - 365
[45] Fourth order linearly recurrent Wythoff pairs
Stolarsky, KB
RAMANUJAN JOURNAL, 1998, 2 (04): : 441 - 448
[46] RECURRENT SEQUENCES AND DENSITY
BATUT, C
COMPTES RENDUS HEBDOMADAIRES DES SEANCES DE L ACADEMIE DES SCIENCES SERIE A, 1975, 281 (2-3): : 57 - 58
[47] Tropical recurrent sequences
Grigoriev, Dima
ADVANCES IN APPLIED MATHEMATICS, 2020, 116
[48] Linearly Recurrent Autoencoder Networks for Learning Dynamics
Otto, Samuel E.
Rowley, Clarence W.
SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS, 2019, 18 (01): : 558 - 593
[49] Fourth Order Linearly Recurrent Wythoff Pairs
Kenneth B. Stolarsky
The Ramanujan Journal, 1998, 2 : 441 - 448
[50] On the Euler function of repdigits
Luca, Florian
CZECHOSLOVAK MATHEMATICAL JOURNAL, 2008, 58 (01) : 51 - 59

← 1 2 3 4 5 →