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writing number in 7x7 board

Source: Ukraine 1999 Grade 8 P2

May 9, 2021
number theorycombinatorics

Problem Statement

Is it possible to write numbers in the cells of a 7×77\times7 board in such a way that the sum of numbers in every 2×22\times2 or 3×33\times3 square is divisible by 19991999, but the sum of all numbers in the board is not divisible by 19991999?
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