Abstract
Let (F-n)(n >= 0) be the Fibonacci sequence given by F-0 = 0, F-1 =1 and Fn+2 = Fn+1 + F-n, for all n >= 0. In this paper, we find all positive integer solutions (m, n, a, k) of the Diophantine equation F-n +/- a(10(m)-1)/9 = k! with 1 <= a <= 9. Our proof requires lower bounds for nonzero linear forms in two logarithms of algebraic numbers both in the complex and p-adic cases and some computer calculations. (C) 2022 Elsevier Inc. All rights reserved.