matrices with integers and difference between 2 adjacent entries <=N
Source: Mexican Mathematical Olympiad 2005 OMM P2
July 31, 2018
matrixIntegerscombinatoricsnumber theory
Problem Statement
Given several matrices of the same size. Given a positive integer , let's say that a matrix is -balanced if the entries of the matrix are integers and the difference between any two adjacent entries of the matrix is less than or equal to .
(i) Show that every -balanced matrix can be written as a sum of two -balanced matrices.
(ii) Show that every -balanced matrix can be written as a sum of three -balanced matrices.