[ $\underline{\text { Modular Arithmetic (other). ] }}$ [Periodicity and Non-periodicity ] Find the remainder of the division by 17 of the number $2^{1999}+1$.
$2^{1999}+1=8 \cdot 16^{499} \equiv 8 \cdot(-1)^{499}=-8 \equiv 9(\bmod 17)$.

## Answer

9.