MathDB

Amy and Bob play the game. At the beginning, Amy writes down a positive integer on the board. Then the players take moves in turn, Bob moves first. On any move of his, Bob replaces the number

n

on the blackboard with a number of the form

n-a^2

, where

a

is a positive integer. On any move of hers, Amy replaces the number

n

on the blackboard with a number of the form

n^k

, where

k

is a positive integer. Bob wins if the number on the board becomes zero. Can Amy prevent Bob’s win?
Maxim Didin, Russia

Problem Statement