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Products of Fermat or Mersenne numbers in some sequences

Mohamadou Bachabi ; Institut de Mathematiques et de Sciences Physiques (IMSP), Universite d’Abomey-Calavi (UAC), Dangbo, Benin
Alain Togbé ; Department of Mathematics and Statistics, Purdue University Northwest, Hammond, USA


Puni tekst: engleski pdf 154 Kb

str. 265-285

preuzimanja: 187

citiraj


Sažetak

Let Pn be an n-th Padovan number, En an n-th Perrin number, and Nn an n-th Nayarana number. In this paper, we solve the Diophantine equations
Pn=(2a1)(2b1),
En=(2a1)(2b1,
and Nn=(2a±1)(2b±1),
in positive unknowns n, a, and b. Therefore, we determine the Padovan or Perrin numbers that are products of two Mersenne numbers and the Nayarana numbers that are Mersenne numbers and two Fermat numbers.

Ključne riječi

Diophantine equations, Padovan sequence, Perrin sequence, Narayana sequence, linear forms in logarithms, reduction method

Hrčak ID:

321269

URI

https://hrcak.srce.hr/321269

Datum izdavanja:

7.10.2024.

Posjeta: 318 *

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