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Combinatorics+Number Theory and a bord to solve

Source: 2023 Girls in Mathematical Tournament- Level A, Problem 4

October 29, 2023
combinatoricsnumber theory

Problem Statement

Determine all nn positive integers such that exists an n×nn\times n where we can write nn times each of the numbers from 11 to nn (one number in each cell), such that the nn sums of numbers in each line leave nn distinct remainders in the division by nn, and the nn sums of numbers in each column leave nn distinct remainders in the division by nn.
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