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TOT 317 1991 Autumn A S3 numbers in 9x9 table

Source:

June 9, 2024
number theorycombinatorics

Problem Statement

Is it possible to put distinct positive integers less than 19911991 in the cells of a 9×99\times 9 table so that the products of all the numbers in every column and every row are equal to each other?
(N.B. Vasiliev, Moscow)