Problem

Source: Azerbaijan EGMO TST 2021, D1 P1

Tags: combinatorics, AZE EGMO TST



Let $n$ be an even positive integer. There are $n$ real numbers written on the blackboard. In every step, we choose two numbers, erase them, and replace each of them with their product. Show that for any initial $n$-tuple it is possible to obtain $n$ equal numbers on the blackboard after a finite number of steps.