3. Find the smallest $n>2016$, such that $1^{n}+2^{n}+3^{n}+4^{n}$ is not divisible by 10.
Answer: 2020.

Solution: Powers of 1 always end in 1. The last digit of powers of 2 changes with a period of 4: 2,4,8,6. Powers of 3 also change with a period of 4: 3,9,7,1. Powers of 4 change with a period of 2: 4,6,4,6. That is, the last digit will repeat with a period of 4. Checking for $n=1,2,3$ we get that the last digit is 0, and for $n=4-4$. Therefore, the smallest N>2016 will be 2020.