MathDB

Integers are written in the cells of a table

2010 \times 2010

. Adding

1

to all the numbers in a row or in a column is called a move. We say that a table is equilibrium if one can obtain after finitely many moves a table in which all the numbers are equal.
[*]Find the largest positive integer

n

, for which there exists an equilibrium table containing the numbers

2^0, 2^1, \ldots , 2^n

. [*] For this

n

, find the maximal number that may be contained in such a table.

Problem Statement