Abstract
AbstractIn this paper, we consider the Diophantine equation $$ V_n - b^m = c $$
V
n
-
b
m
=
c
for given integers b, c with $$ b \ge 2 $$
b
≥
2
, whereas $$ V_n $$
V
n
varies among Lucas-Lehmer sequences of the second kind. We prove under some technical conditions that if the considered equation has at least three solutions (n, m) , then there is an upper bound on the size of the solutions as well as on the size of the coefficients in the characteristic polynomial of $$ V_n $$
V
n
.
Publisher
Springer Science and Business Media LLC