Revista Integración, temas de matemáticas.

Revista Integración, temas de matemáticas

Vol. 41 No. 2 (2023): Revista Integración, temas de matemáticas
Research and Innovation Articles

The Padovan numbers of the form 6a ± 6 b ± 6 c

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Ana Cecilia García Lomelí
Centro de Investigación en Matemáticas (CIMAT), Unidad Zacateca
Santos Hernández Hernández
Universidad Aut\'onoma de Zacatecas, Campus II
DOI: https://doi.org/10.18273/revint.v41n2-2023001

Published 2023-09-06

How to Cite

García Lomelí, A. C., & Hernández Hernández, S. (2023). The Padovan numbers of the form 6a ± 6 b ± 6 c. Revista Integración, Temas De matemáticas, 41(2), 69–81. https://doi.org/10.18273/revint.v41n2-2023001

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Abstract

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.

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