RU-ALLRUSSIAN 1984 Problem 20
The squares of a 1983 x 1984 chess board are colored alternately black and white in the usual way. Each white square is given the number 1 or the number - 1. For each black square the product of the numbers in the neighbouring white squares is 1. Show that all the numbers must be 1.
Dataset text NuminaMath olympiads. Quoted with source.
Solutions
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