Resumo

GARCIA LOMELI, ANA CECILIA  e  HERNANDEZ HERNANDEZ, SANTOS. Pillai's problem with Padovan numbers and powers of two. Rev.colomb.mat. [online]. 2019, vol.53, n.1, pp.1-14. ISSN 0034-7426.

Let (P n ) n≥0 be the Padovan sequence given by P 0 = 0, P 1 = P 2 = 1 and the recurrence formula P n+3 = P n+1 + P n for all n ≥ 0. In this note we study and completely solve the Diophantine equation P n - 2 m = P n1 -2 m1 in non-negative integers (n,m,n 1 ,m 1 ).

Palavras-chave : Padovan sequence; Pillai's problem; linear forms in logarithms; reduction method.

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