MathDB

A positive integer is written on a blackboard. Players

A

and

B

play the following game: in each move one has to choose a proper divisor

m

of the number

n

written on the blackboard (

1<m<n

) and replaces

n

with

n-m

. Player

A

makes the first move, then players move alternately. The player who can't make a move loses the game. For which starting numbers is there a winning strategy for player

B

Problem Statement