Problem 5
Source: All-Russian Olympiad 2019 grade 10 Problem 5
April 24, 2019
rectanglenumber theoryprime numbers
Problem Statement
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.