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1 or -1 in n x n cells - All-Russian MO 1996 Regional (R4) 10.4

Source:

September 23, 2024

combinatorics

Problem Statement

In each cell of a square table of size

n \times n

cells (

n \ge 3

) the number

1

-1

is written. If you take any two lines, multiply numbers standing above each other in them and add the n resulting products, then the sum will be equal to

0

. Prove that the number

n

is divisible by

4

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