MathDB

A 3x3 magic square, with magic number

m

, is a

3\times 3

matrix such that the entries on each row, each column and each diagonal sum to

m

. Show that if the square has positive integer entries, then

m

is divisible by

3

, and each entry of the square is at most

2n-1

, where

m=3n

. An example of a magic square with

m=6

\left( \begin{array}{ccccc} 2 & 1 & 3\\ 3 & 2 & 1\\ 1 & 3 & 2 \end{array} \right)

Problem Statement