Common values of a class of linear recurrences

Let (an), (bn) be linear recursive sequences of integers with characteristic polynomials A(X), B(X) is an element of Z[X] respectively. Assume that A(X) has a dominating and simple real root alpha, while B(X) has a pair of conjugate complex dominating and simple roots C, C over line . Assume further that alpha, C, alpha/C and C over line /C are not roots of unity and delta = log |C|/log |alpha| is an element of Q. Then there are effectively computable constants c0, c1 > 0 such that the inequality|an - bm| > |an|1-(c0 log2 n)/nholds for all n, m is an element of Z2 >= 0 with max{n, m} > c1. We present c0 explicitly.(c) 2022 Royal Dutch Mathematical Society (KWG). Published by Elsevier B.V. All rights reserved.