3. (3 points) The number 2017 is written on the board. Petya and Vasya are playing the following game: in one move, they can subtract any natural divisor of the number written on the board, except the number itself, and write the result of this subtraction on the board instead of the original number. Petya starts. The one who cannot make a move loses. Who wins with correct play?

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# Answer: Vasya

Solution: It is impossible to make a move only if the number on the board is one. At the same time, an odd number always turns into an even number. Vasya, receiving an even number, can always subtract 1 and get an odd number again. Thus, Vasya can always receive even numbers from Petya and give him odd numbers, while Petya, on the contrary, will not have another option. Eventually, Vasya will get 1 as a result of his subtraction, and Petya will not be able to make a move.