Question 64
Luk was bored during math class, so he first drew a circle and then $n$ empty fields around the perimeter, where $n \geq 3$, and wrote 1 positive number in each of them. Later, he erased these numbers, and wrote in each field the square root of the product of two numbers that previously lay in that field of neighboring fields. Show that there is a field in which the number written is less than or equal to the one written before.