MathDB

Given a

m \times n

rectangle where

m,n\geq 2023

. The square in the

i

-th row and

j

-th column is filled with the number

i+j

for

1\leq i \leq m, 1\leq j \leq n

. In each move, Alice can pick a

2023 \times 2023

subrectangle and add

1

to each number in it. Alice wins if all the numbers are multiples of

2023

after a finite number of moves. For which pairs

(m,n)

can Alice win?
Proposed by Boon Qing Hong

5