MathDB

In a game, Andi and a computer take turns. At the beginning, the computer shows a polynomial

x^2 + mx + n

where

m,n \in \mathbb{Z}

, such that it doesn't have real roots. Andi then begins the game. On his turn, Andi may change a polynomial in the form

x^2 + ax + b

into either

x^2 + (a+b)x + b

x^2 + ax + (a+b)

. However, Andi may only choose a polynomial that has real roots. On the computer's turn, it simply switches the coefficient of

x

and the constant of the polynomial. Andi loses if he can't continue to play. Find all

(m,n)

such that Andi always loses (in finitely many turns).

Problem Statement