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positive integers in every cell of a 10 x10 array

Source: New Zealand MO 2021 Round 1 p6

September 20, 2021
combinatoricsconsecutivenumber theorydivisor

Problem Statement

Is it possible to place a positive integer in every cell of a 10×1010 \times 10 array in such a way that both the following conditions are satisfied? ∙\bullet Each number (not in the top row) is a proper divisor of the number immediately above. ∙\bullet Each row consists of 100 consecutive positive integers (but not necessarily in order).
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