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TOT 306 1991 Autumn A J3 numbers in a 4x4 table

Source:

June 9, 2024
algebracombinatorics

Problem Statement

Is it possible to put pairwise distinct positive integers less than 100100 in the cells of a 4×44 \times 4 table so that the products of all the numbers in every column and every row are equal to each other?
(N.B. Vasiliev, Moscow))
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