Affiliation:
1. Department of Mathematics, Sambalpur University , Jyoti Vihar , Burla , INDIA
Abstract
ABSTRACT
The Padovan sequence {Pn
}
n≥0 is a ternary recurrent sequence defined recursively by the relation Pn
= P
n–2 + P
n–3 with initials P
0 = P
1 = P
2 = 1. In this note, we search all pairs of multiplicative dependent vectors whose coordinates are Padovan numbers. For this purpose, we apply Matveev’s theorem to find the lower bounds of the non-zero linear forms in logarithms. Techniques involving the LLL algorithm and the theory of continued fraction are utilized to reduce the bounds.
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