Finding a subsquare from the main square
Source: Iran 3rd round 2012-Special Lesson exam-Part 2-P4
September 15, 2012
linear algebramatrixcombinatorics proposedcombinatorics
Problem Statement
Prove that if is large enough, in every square that a natural number is written on each one of its cells, one can find a subsquare from the main square such that the sum of the numbers is this subsquare is divisible by .