Coincidence Between k-Fibonacci Numbers and Products of Two Fermat Numbers

被引：3

作者：

Gueye, Alioune ^{[1
]}

Rihane, Salah Eddine ^{[2
]}

Togbe, Alain ^{[3
]}

机构：

[1] Univ Gaston Berger, UFR Appl Sci & Technol, St Louis, Senegal

[2] Univ Ctr Mila, Inst Sci & Technol, Dept Math, Mila, Algeria

[3] Purdue Univ Northwest, Dept Math Stat & Comp Sci, 1401 S,US 421, Westville, IN 46391 USA

来源：

BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY | 2022年 / 53卷 / 02期

关键词：

k-Fibonacci numbers; Fermat numbers; Linear form in logarithms; Reduction method;

D O I：

10.1007/s00574-021-00269-2

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let k >= 2. A generalization of the well-known Fibonacci sequence is the k-Fibonacci sequence. For this sequence, the first k terms are 0, ..., 0, 1 and each term afterwards is the sum of the preceding k terms. In this paper, we find all k-Fibonacci which are product of two Fermat numbers.

引用

页码：541 / 552

页数：12

共 50 条

[1] Coincidence Between k-Fibonacci Numbers and Products of Two Fermat Numbers
Alioune Gueye
Salah Eddine Rihane
Alain Togbé
[J]. Bulletin of the Brazilian Mathematical Society, New Series, 2022, 53 : 541 - 552
[2] On Fermat and Mersenne numbers expressible as product of two k-Fibonacci numbers
Mohand O. Hernane
Salah Eddine Rihane
Safia Seffah
Alain Togbé
[J]. Boletín de la Sociedad Matemática Mexicana, 2022, 28
[3] On Fermat and Mersenne numbers expressible as product of two k-Fibonacci numbers
Hernane, Mohand O.
Rihane, Salah Eddine
Seffah, Safia
Togbe, Alain
[J]. BOLETIN DE LA SOCIEDAD MATEMATICA MEXICANA, 2022, 28 (02):
[4] FERMAT k-FIBONACCI AND k-LUCAS NUMBERS
Bravo, Jhon J.
Herrera, Jose L.
[J]. MATHEMATICA BOHEMICA, 2020, 145 (01): : 19 - 32
[5] Repdigits as sums of two k-Fibonacci numbers
Bravo, Jhon J.
Luca, Florian
[J]. MONATSHEFTE FUR MATHEMATIK, 2015, 176 (01): : 31 - 51
[6] POWERS OF TWO AS SUMS OF TWO k-FIBONACCI NUMBERS
Bravo, Jhon J.
Gomez, Carlos A.
Luca, Florian
[J]. MISKOLC MATHEMATICAL NOTES, 2016, 17 (01) : 85 - 100
[7] On the complex k-Fibonacci numbers
Falcon, Sergio
[J]. COGENT MATHEMATICS, 2016, 3
[8] MERSENNE k-FIBONACCI NUMBERS
Bravo, Jhon J.
Gomez, Carlos A.
[J]. GLASNIK MATEMATICKI, 2016, 51 (02) : 307 - 319
[9] Recurrences for k-Fibonacci Numbers
Linders, J. C.
[J]. AMERICAN MATHEMATICAL MONTHLY, 2011, 118 (04): : 374 - 376
[10] On the powers of the k-Fibonacci numbers
Falcon, Sergio
[J]. ARS COMBINATORIA, 2016, 127 : 329 - 338

← 1 2 3 4 5 →