Sum of all numbers is divisible by 13
Source: Saint Petersburg olympiad 2024, 10.1
September 22, 2024
combinatoricsnumber theory
Problem Statement
In the cells of the board, integers are arranged so that in any rectangle (vertical or horizontal) with one cut corner cell that does not go beyond the board, the sum of the numbers is divided by . Prove that the sum of all the numbers on the board is divisible by .