MathNet 2016-part-06 — 184 problems (EN–VI) Question 131

There are $2016$ real numbers written on the blackboard. In each step, we choose two numbers, erase them, and replace each of them by their product. Determine whether it is possible to obtain $2016$ equal numbers on the blackboard after a finite number of steps.

(the 15th Czech-Polish-Slovak Mathematics Competition)