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Integers in Infinite Chessboard

Source: All-Russian MO 2003 Grade 11 #6

January 2, 2012
geometryrectangleanalytic geometrycombinatorics unsolvedcombinatorics

Problem Statement

Is it possible to write a positive integer in every cell of an infinite chessboard, in such a manner that, for all positive integers m,nm, n, the sum of numbers in every m×nm\times n rectangle is divisible by m+nm + n ?
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