RU-ALLRUSSIAN 2019 Problem 105
In a kindergarten, a nurse took congruent cardboard rectangles and gave them to kids, one per each. Each kid has cut its rectangle into congruent squares(the squares of different kids could be of different sizes). It turned out that the total number of the obtained squares is a prime number. Prove that all the initial squares were in fact squares.
Dataset text AI-MO AoPS. Quoted with source.
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