2. (5 points) Find the remainder when $20^{16}+201^{6}$ is divided by 9.
Answer: 7

Solution. $201^{16}$ is divisible by 9. 20 gives a remainder of $2.2^{6}$ gives a remainder of $1,2^{16}=2^{6} \cdot 2^{6} \cdot 2^{4}$ gives the same remainder as 16.