MathDB

In each unit cell of a finite set of cells of an infinite checkered board, an integer is written so that the sum of the numbers in each row, as well as in each column, is divided by

2002

. Prove that every number

\alpha

can be replaced by a certain number

\alpha'

, divisible by

2002

so that

|\alpha-\alpha'| <2002

and the sum of the numbers in all rows, and in all columns will not change.

Problem Statement