Question 76
Polynomial $x^{1398} + 1$ is written on the board. Roozbeh and Keyvan play the following game in turns. Starting from Roozbeh, each player in their turn chooses an integer $0 \le k \le 1398$ and adds up $x^k$ with the polynomial on the board. Each time after Keyvan's turn, if there exists a real number $x$ such that the polynomial on the board takes negative value,
Roozbeh wins and Keyvan loses. Otherwise, the game continues. Prove that no matter how Roozbeh plays, Keyvan can play in a way that he never loses.
Roozbeh wins and Keyvan loses. Otherwise, the game continues. Prove that no matter how Roozbeh plays, Keyvan can play in a way that he never loses.