Berdnikov A.

Sasha writes a sequence of natural numbers on the board. The first number $N>1$ is written in advance. New natural numbers he gets by subtracting from the last written number or adding to it any of its divisors greater than 1. Can Sasha write the number 2011 on the board at some point for any natural $N>1$?
First method. By adding $N$ each time, we get 2011N. By subtracting 2011 each time, we get 2011.

Second method. If $N$ is odd, add $N$ and get an even number. By adding or subtracting twos from it, we get 4022. Subtracting 2011, we get 2011.

## Answer

For any.