MathDB

Let

m

be a positive integer. Two players, Axel and Elina play the game HAUKKU (

m

) proceeds as follows: Axel starts and the players choose integers alternately. Initially, the set of integers is the set of positive divisors of a positive integer

m

.The player in turn chooses one of the remaining numbers, and removes that number and all of its multiples from the list of selectable numbers. A player who has to choose number

1

, loses. Show that the beginner player, Axel, has a winning strategy in the HAUKKU (

m

) game for all

m \in Z_{+}

.
PS. As member Loppukilpailija noted, it should be written

m>1

, as the statement does not hold for

m = 1

Problem Statement