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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
Sažetak
Let \(P_{n}\) be an n-th Padovan number, \(E_{n}\) an n-th Perrin number, and \(N_{n}\) an n-th Nayarana 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 \(N_{n}=(2^{a} \pm 1)(2^{b}\pm 1),\)
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
Hrčak ID:
321269
URI
Datum izdavanja:
7.10.2024.
Posjeta: 158 *