All natural numbers greater than one were painted in two colors - blue and red - such that the sum of any two blue numbers (including identical ones) is blue, and the product of any two red numbers (including identical ones) is red. It is known that both colors were used in the painting and that the number 1024 was painted blue. What color could the number 2017 be in this case?

#
Note that if the number $b^{n}$ is blue, then the number $b$ is also blue. Since $1024=2^{10}$, the number 2 is blue. From this, it follows that all even numbers are blue, and also that if a number $a>4$ is red, then $a-2$ is also red.

Consider an arbitrary red number $k$. Then any power of $k$ is also red. Since $k>2$, there exists a power of $k$ that exceeds 2017. By subtracting the necessary number of twos, we get that 2017 is a red number.

## Answer

Red.