# Thread: finding the remainder by mod

1. ## finding the remainder by mod

what is the remainder when 2 to the power of 61 is divided by 13?

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