On a Class of Congruences for Lucas Sequences

Abstract

Let ⋋,µ∈ℤ and define a sequence of integers {H_n(λ,μ)}_n≥0 by the linear recurrence

$$ {H_0}\left( {\lambda ,\mu } \right) = 2,{H_1}\left( {\lambda ,\mu } \right) = \lambda ,and{H_{n + 1}}\left( {\lambda ,\mu } \right) = \lambda {H_n}\left( {\lambda ,\mu } \right) + \mu {H_{n - 1}}\left( {\lambda ,\mu } \right)forn > 0. $$

((1.1))