On the solutions of the Diophantine equation F_{n_۱}+F_{n_۲}+F_{n_۳}+F_{n_۴}=۱۱^a

Let F_{n} denote the nth Fibonacci number‎. ‎In this paper‎, ‎we solve the Diophantine equation F_{n_۱}+F_{n_۲}+F_{n_۳}+F_{n_۴}=y^a in integers n_۱,n_۲,n_۳,n_۴,a for y=۱۱‎. ‎In doing so‎, ‎we disprove a recent conjecture made by Diouf and Tiebekabe in \cite{D-T}‎.

کلیدواژه ها:

Linear recurrences‎ ، ‎Exponential Diophantine problems‎ ، ‎Baker's method