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n x n square filled with

Source: 239 2001 J1

May 20, 2020
combinatorics

Problem Statement

A square n×n n \times n , (n>2 n> 2 ) contains nonzero real numbers. It is known that every number is exactly k k times smaller than the sum of all the numbers in its row or sum of all number in its column. For which real numbers k k is this possible?
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