tiling by dominoes and coprime numbers
Source: RS2004
March 20, 2005
number theorycombinatorics proposedcombinatorics
Problem Statement
An chessboard is completely tiled by dominoes. Prove that we can place positive integers
in all cells of the table in such a way that the sums of numbers in every domino are equal and the numbers placed
in two adjacent cells are coprime if and only if they belong to the same domino. (Two cells are called adjacent if
they have a common side.)
Well this can belong to number theory as well...