two numbers replaced with their product
Source: Azerbaijan EGMO TST 2021, D1 P1
August 11, 2023
combinatoricsAZE EGMO TST
Problem Statement
Let be an even positive integer. There are 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 -tuple it is possible to obtain equal numbers on the blackboard after a finite number of steps.