MathDB
Integral arithmetic means

Source: Czech and Slovak Olympiad 2019, National Round, Problem 6

June 7, 2019
Combinatorial Number Theorynumbers in a tablenational olympiadnumber theory

Problem Statement

Assume we can fill a table n×nn\times n with all numbers 1,2,…,n2−1,n21,2,\ldots,n^2-1,n^2 in such way that arithmetic means of numbers in every row and every column is an integer. Determine all such positive integers nn.
Back to ProblemsView on AoPS