# Divisibility of Terms in Lucas Sequences by Their Subscripts

@inproceedings{Somer1993DivisibilityOT, title={Divisibility of Terms in Lucas Sequences by Their Subscripts}, author={L. Somer}, year={1993} }

Let (U) = U(P,Q) be a Lucas sequence of the first kind (LSFK) satisfying the second-order relation
$$U_{n + 2} = PU_{n + 1} - QU_n$$
(1)
and having initial terms U 0 = 0, U 1 = 1, where P and Q are integers. Let D = P 2 − 4Q be the discriminant of U(P,Q). Associated with U(P,Q) is the characteristic polynomial
$$f(x) = x^2 - Px + Q$$
(2)
with characteristic roots α and β. By the Binet formula
$$U_n = (\alpha ^n - \beta ^n )/(\alpha - \beta )$$
(3)
if D ≠ 0. It is also… Expand

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Index Divisibility in the Orbit of 0 for Integral Polynomials

- Mathematics, Computer Science
- Integers
- 2020

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