IMO 2010 Shortlist N6
The rows and columns of a 2n 2n table are numbered from 0 to 2n 1. The cells of the table have been colored with the f...
Category: Number Theory
Problem
The rows and columns of a 2n 2n table are numbered from 0 to 2n 1. The cells of the table have been colored with the following property being satisfied: for each 0 ¨i,j ¨2n 1, the jth cell in the ith row and the pi jqth cell in the jth row have the same color. (The indices of the cells in a row are considered modulo 2n .) Prove that the maximal possible number of colors is 2n . (Iran)