Products of Fermat or Mersenne numbers in some sequences

被引：0

作者：

Bachabi, Mohamadou ^{[1
]}

Togbe, Alain S. ^{[2
]}

机构：

[1] Univ Abomey Calavi UAC, Inst Math & Sci Phys IMSP, Dangbo, Benin

[2] Purdue Univ Northwest, Dept Math & Stat, 2200 169th St, Hammond, IN 46323 USA

来源：

MATHEMATICAL COMMUNICATIONS | 2024年 / 29卷 / 02期

关键词：

Diophantine equations; Padovan sequence; Perrin sequence; Narayana sequence; linear forms in logarithms; reduction method; FIBONACCI; EQUATIONS; INTERSECTION;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let P-n be an n-th Padovan number, E-n an n-th Perrin number, and N-n an n-th Narayana number. In this paper, we solve the Diophantine equations P-n = (2(a) -1)(2(b) - 1), E-n = (2(a )-1)(2(b) - 1), and N-n = (2(a) +/- 1)(2(b) +/- 1), in positive integers n, a and b . Therefore, we determine the Padovan or Perrin numbers that are products of two Mersenne numbers and the Narayana numbers that are products of two Mersenne or Fermat numbers.

引用

页码：265 / 285

页数：21

共 50 条

[21] On Mulatu and generalized Lucas numbers which are products of four b-repdigits with a consequence
Adedji, Kouessi Norbert
[J]. INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS, 2025,
[22] Repdigits base b as products of two Pell numbers or Pell-Lucas numbers
Erduvan, Fatih
Keskin, Refik
Siar, Zafer
[J]. BOLETIN DE LA SOCIEDAD MATEMATICA MEXICANA, 2021, 27 (03):
[23] Algebra of quaternions and octonions involving higher order Mersenne numbers
Kumari, Munesh
Prasad, Kalika
Mohanta, Rabiranjan
[J]. PROCEEDINGS OF THE INDIAN NATIONAL SCIENCE ACADEMY, 2024, 91 (1): : 333 - 342
[24] Fibonacci numbers which are products of two Jacobsthal numbers
Erduvan, Fatih
Keskin, Refik
[J]. TBILISI MATHEMATICAL JOURNAL, 2021, 14 (02) : 105 - 116
[25] Fibonacci numbers which are products of two balancing numbers
Erduvan, Fatih
Keskin, Refik
[J]. ANNALES MATHEMATICAE ET INFORMATICAE, 2019, 50 : 57 - 70
[26] Fibonacci and Lucas numbers as products of three repdgits in base g
Kouèssi Norbert Adédji
Alan Filipin
Alain Togbé
[J]. Rendiconti del Circolo Matematico di Palermo Series 2, 2023, 72 : 4003 - 4021
[27] Fibonacci and Lucas numbers as products of three repdgits in base g
Adedji, Kouessi Norbert
Filipin, Alan
Togbe, Alain
[J]. RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO, 2023, 72 (08) : 4003 - 4021
[28] PADOVAN AND PERRIN NUMBERS AS PRODUCTS OF TWO GENERALIZED LUCAS NUMBERS
Adedji, Norbert Kouessi
Odjoumani, Japhet
Togbe, Alain
[J]. ARCHIVUM MATHEMATICUM, 2023, 59 (04): : 315 - 337
[29] FERMAT k-FIBONACCI AND k-LUCAS NUMBERS
Bravo, Jhon J.
Herrera, Jose L.
[J]. MATHEMATICA BOHEMICA, 2020, 145 (01): : 19 - 32
[30] Padovan and Perrin Numbers Which are Products of Two Repdigits in Base b
Kouèssi Norbert Adédji
Alan Filipin
Alain Togbé
[J]. Results in Mathematics, 2021, 76

← 1 2 3 4 5 →