Abstract
AbstractLet $$ \{U_n\}_{n\ge 0} $$
{
U
n
}
n
≥
0
be the Lucas sequence. For integers x, n and m, we find all solutions to $$U_{n}^x+U_{n+1}^x=U_m$$
U
n
x
+
U
n
+
1
x
=
U
m
. The equation was studied and claimed to be solved completely in Ddamulira and Luca (Ramanujan J 56(2):651–684, 2021) but there are some computational bugs in that publication because of the wrong statement of Mignotte’s bound from Mignotte (A kit on linear forms in three logarithms. http://irma.math.unistra.fr/~bugeaud/travaux/kit.pdf, 2008). In this paper, the main result remains the same as in Ddamulira and Luca (Ramanujan J 56(2):651–684, 2021) but we focus on correcting the computational mistakes in Ddamulira and Luca (Ramanujan J 56(2):651–684, 2021), involving the application of Theorem 2.1 from Mignotte (A kit on linear forms in three logarithms. http://irma.math.unistra.fr/~bugeaud/travaux/kit.pdf, 2008).
Funder
University of the Witwatersrand
Publisher
Springer Science and Business Media LLC
Subject
Algebra and Number Theory
Reference7 articles.
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