MathDB

Initially, the number

1

and a non-integral number

x

are written on a blackboard. In each step, we can choose two numbers on the blackboard, not necessarily different, and write their sum or their difference on the blackboard. We can also choose a non-zero number of the blackboard and write its reciprocal on the blackboard. Is it possible to write

x^2

on the blackboard in a finite number of moves?

Problem Statement