quadratic will have integer roots
Source: INMO 2014- Problem 4
February 2, 2014
quadraticsalgebrapolynomialcalculusintegrationprobabilityanalytic geometry
Problem Statement
Written on a blackboard is the polynomial . Calvin and Hobbes take turns alternately (starting with Calvin) in the following game. At his turn, Calvin should either increase or decrease the coefficient of by . And at this turn, Hobbes should either increase or decrease the constant coefficient by . Calvin wins if at any point of time the polynomial on the blackboard at that instant has integer roots. Prove that Calvin has a winning stratergy.