Аннотация:For a positive integer k ≥ 3 let (u_m^(k))m≥0 be the Lucas sequence given by
u_0^(k) = 0, u_1^(k) = 1
and
u_{m+2}^(k) = ku_{m+1}^(k) − u_m^(k)
for all m ≥ 0. In this paper, we study the positive integers n such that
(n − k)/(1 + (k − 2)(u_m^(k))²)∉ℤ
for any 3 ≤ k < n and m ≥ 1.