what is the remainder when 2 to the power of 61 is divided by 13?
You want to reduce $\displaystyle 2^{61}$ mod $\displaystyle 13$.
Begin with, $\displaystyle 2^{12} \equiv 1 ~ (13)$.
Raise to the 5th to get $\displaystyle 2^{60} \equiv 1 ~ (13)$.
Thus, what doth this mean?