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write a natural number in all cell of an infinite chessboard

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November 3, 2010
geometryrectanglecombinatorics proposedcombinatorics

Problem Statement

Is it possible to write a natural number in every cell of an infinite chessboard in such a manner that for all integers m,n>100m, n > 100, the sum of numbers in every m×nm\times n rectangle is divisible by m+n ?m + n \ ?
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