5. Find all natural numbers $N$ such that the remainder of dividing 2017 by $N$ is 17. In your answer, specify the number of such $N$.

ANSWER 13.
Solution - As $N$, all positive divisors of the number 2000 greater than 17 will work. The divisors of 2000 have the form $2^{a} \cdot 5^{b}$, where $a=0,1,2,3,4$ and $b=0,1,2,3$. There will be 20 of them in total, but we need to exclude $1,2,4,5,8,10$ and 16.