MathDB

6

Part of 2019 Czech and Slovak Olympiad III A

Problems(1)

Integral arithmetic means

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

6/7/2019
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.
Combinatorial Number Theorynumbers in a tablenational olympiadnumber theory