Given a pair (
Ut) and (
Vt) of Lucas sequences, Kimball and Webb
showed that
![$\sum_{0<t<\rho_U}\frac{V_t}{U_t} \equiv 0$](img1.gif)
(mod
p2), if
p is a prime
![$\ge5$](img2.gif)
whose rank
![$\rho_U$](img3.gif)
is maximal, that is to say,
![$\rho_U$](img3.gif)
is
p or
![$p\pm1$](img4.gif)
.
We extend their result replacing
p by a
composite integer
m of maximal rank, thereby providing a
generalization of a classical congruence of Leudesdorf.