Question 85
Two players play the following game. They start with the polynomial $2013x^2 + 2012x + 2011$ and take moves by turns. During each move a player subtracts from the polynomial one of the following polynomials: $x^2$, $x$, $x^2 - x + 1$ or $x^2 + x - 1$, at his choice. If after a player's move the polynomial has an integer root, he loses. Which of the players has a winning strategy?