The match on the equation ax^2 + bx + c = 0 - always win
Source:
June 14, 2011
quadraticsalgebra
Problem Statement
Johnny writes down quadratic equation
with positive integer coefficients . Then Pete changes one, two, or none “” signs to “”. Johnny wins, if both roots of the (changed) equation are integers. Otherwise (if there are no real roots or at least one of them is not an integer), Pete wins. Can Johnny choose the coefficients in such a way that he will always win?