A natural number n is written on a board. On every step, Neneng and Asep changes the number on the board with the following rule: Suppose the number on the board is X. Initially, Neneng chooses the sign up or down. Then, Asep will pick a positive divisor d of X, and replace X with X+d if Neneng chose the sign "up" or X−d if Neneng chose "down". This procedure is then repeated. Asep wins if the number on the board is a nonzero perfect square, and loses if at any point he writes zero.Prove that if n≥14, Asep can win in at most (n−5)/4 steps. combinatoricsGame TheoryPerfect SquareIndonesiaIndonesia MO