MathDB

Ivan and Kolya play a game, Ivan starts. Initially, the polynomial

x-1

is written of the blackboard. On one move, the player deletes the current polynomial

f(x)

and replaces it with

ax^{n+1}-f(-x)-2

, where

\deg(f)=n

and

a

is a real root of

f

. The player who writes a polynomial which does not have real roots loses. Can Ivan beat Kolya?

Problem Statement