On the exponential diophantine equation $U_{n}^x+U_{n+1}^x=U_m$

Let $$ \{U_n\}_{n\ge 0} $${ 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).