2018 PAMO Shortlist: Players take turns choosing coefficients of a polynomial
Source: 2018 Pan-African Shortlist - C2
May 7, 2019
gamecombinatoricspolynomialinteger rootalgebra
Problem Statement
Adamu and Afaafa choose, each in his turn, positive integers as coefficients of a polynomial of degree . Adamu wins if the polynomial obtained has an integer root; otherwise, Afaafa wins. Afaafa plays first if is odd; otherwise Adamu plays first. Prove that:[*] Adamu has a winning strategy if is odd.
[*] Afaafa has a winning strategy if is even.