Two players want to obtain a number divisible by 2023
Source: All-Russian MO 2023 Final stage 11.5
April 23, 2023
number theory
Problem Statement
Initially, ones are written on a blackboard. Grisha and Gleb are playing game, by taking turns; Grisha goes first. On one move Grisha squares some numbers on the board. On his move, Gleb picks a few (perhaps none) numbers on the board and increases each of them by . If in moves on the board a number divisible by appears, Gleb wins, otherwise Grisha wins. Which of the players has a winning strategy?