Abstract

PETHő, Attila  and  SZALAY, László. Upper bound on the solution to F ^(2k) _n = (F ^(2k) _m with negative subscripts. Rev.colomb.mat. [online]. 2022, vol.56, n.2, pp.179-187.  Epub Jan 05, 2024. ISSN 0034-7426.  https://doi.org/10.15446/recolma.v56n2.108374.

In this paper, we provide an explicit upper bound on the absolute value of the solutions n < m < 0 to the Diophantine equation F (k) n = ±F (k) m , assuming k is even. Here {F (k) n } n ∈ Z denotes the k-generalized Fibonacci sequence. The upper bound depends only on k.

Keywords : k-generalized Fibonacci sequence; total multiplicity.

        · abstract in Spanish     · text in English     · English ( pdf )