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

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