Abstract

GARCIA LOMELI, ANA CECILIA  and  HERNANDEZ HERNANDEZ, SANTOS. The Padovan numbers of the form 6^a ± 6^b ± 6^c. Integración - UIS [online]. 2023, vol.41, n.2, pp.69-81.  Epub Aug 09, 2023. ISSN 0120-419X.  https://doi.org/10.18273/revint.v41n2-2023001.

Let (Pn)n≥0 be the Padovan sequence given by P0 = 0, P1 = P2 = 1 and the recurrence formula Pn+3 = Pn+1 + Pn for all n≥0. In this note, we completely solve the Diophantine equation Pn = 6a ± 6b ± 6c in non-negative integers (n, a, b, c) with a≥b≥c≥0.

Keywords : Padovan sequence; Linear forms in logarithms; Reduction method.

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