MathDB

Aisling and Brendan take alternate moves in the following game. Before the game starts, the number

x = 2023

is written on a piece of paper. Aisling makes the first move. A move from a positive integer

x

consists of replacing

x

either with

x + 1

or with

x/p

where

p

is a prime factor of

x

.
The winner is the first player to write

x = 1

.
Determine whether Aisling or Brendan has a winning strategy for this game.

Problem Statement