On the Diophantine equation $F_{n}-F_{m}=2^{a}$
On the Diophantine equation $F_{n}-F_{m}=2^{a}$
We solve the Diophantine equation in the tittle in nonnegative integers $m,n,$ and $a$. In order to prove our result, we use lower bounds for linear forms in logarithms and a version of the Baker–Davenport reduction method in Diophantine approximation.