Problem

Source: Slovenia National MO 2005 1st Grade P4

Tags: number theory



The friends Alex, Ben, and Charles prepared a lot of labels and wrote one of the numbers $2,3,4,5,6,7,8$ on each label. Then Mary joined them and glued one label onto the forehead of each friend. Of course, each of the friends can see the labels on the others’ foreheads, but not the one on his own forehead. Mary told them: ”The numbers on your foreheads are not all distinct, and their product is a perfect square.” Can any of the friends find out the number on his forehead?