Problem

Source: (2022 -) 2023 XVI Dürer Math Competition Finals Day 1 E2

Tags: number theory



When Andris entered the room, there were the numbers $3$ and $24$ on the board. In one step, if there are the (not necessarily different) numbers $k$ and $n$ on the board already, then Andris can write the number$ kn + k + n$ on the board, too. a) Can Andris write the number $9999999$ on the board after a few moves? b) What if he wants to get $99999999$? c) And what about $48999999$?