Repdigits as Euler functions of Lucas numbers

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica

Tall Amadou¹  Bravo Jhon J.²  Faye Bernadette³  Luca Florian⁴ 

[1] AIMS-Senegal, Km 2 route de Joal (Centre IRD Mbour), BP: 64566 Dakar-Fann, Senegal;Departamento de Matemäticas, Universidad del Cauca, Calle 5 No 4–70, Popayän, Colombia;School of Mathematics, University of the Witwatersrand, Private Bag X3, Wits 2050, South Africa and AIMS-Sengal, Km 2 route de Joal (Centre IRD Mbour), BP: 64566 Dakar-Fann, Senegal;The John Knopfmacher Centre for Applied Analysis and Number Theory, School of Mathematics, University of the Witwatersrand, Private Bag X3, Wits 2050, Witwatersrand, South Africa;

关键词: fibonacci numbers;    lucas numbers;    applications of linear forms in logarithms;    primary 11b39;    secondary 11d61;   

DOI  :  10.1515/auom-2016-0030

来源: DOAJ

【 摘 要 】

We prove some results about the structure of all Lucas numbers whose Euler function is a repdigit in base 10. For example, we show that if Ln is such a Lucas number, then n < 10111 is of the form p or p2, where p3 | 10p-1 -1.

【 授权许可】

Unknown