Multiplying numbers on the blackboard
Source: Czech-Polish-Slovak Match 2015, Problem 6
June 19, 2015
combinatorics
Problem Statement
Let be even positive integer. There are real positive numbers written on the blackboard. In every step, we choose two numbers, erase them, and replace each of then by their product. Show that for any initial -tuple it is possible to obtain equal numbers on the blackboard after a finite number of steps.Proposed by Peter Novotný