Abstract
AbstractIn this paper we consider the Diophantine equation $$U_n=p^x$$
U
n
=
p
x
where $$U_n$$
U
n
is a linear recurrence sequence, p is a prime number, and x is a positive integer. Under some technical hypotheses on $$U_n$$
U
n
, we show that, for any p outside of an effectively computable finite set of prime numbers, there exists at most one solution (n, x) to that Diophantine equation. We compute this exceptional set for the Tribonacci sequence and for the Lucas sequence plus one.
Publisher
Springer Science and Business Media LLC
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