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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