MathDB
adding reminder of one number to some other to blackboard

Source: 239 2017 J6

June 3, 2020
combinatoricsblackboard

Problem Statement

The natural numbers y>xy>x are written on the board. Vassya decides to write the reminder of one number on the board to some other non-zero number in each step. Prove that Vassya can find a natural number kk such that if y>ky>k then the number distinct numbers on the board after arbitrary number of steps does not exceed y1000000.\frac{y}{1000000}.