ARMO 2019 9.5
Source: All-Russian Math Olympiad 2019
July 12, 2019
ARMO
Problem Statement
In kindergarten, nurse took identical cardboard rectangles and distributed them to children; every child got one rectangle. Every child cut his (her) rectangle into several identical squares (squares of different children could be different). Finally, the total number of squares was prime. Prove that initial rectangles was squares.