Suppse that $n\geq 3$ be an inetegr number and $x\in \mathbb{R}$ s.t. $x,x^2$ and $x^n$ have a same decimal representation. Prove that $x$ is an integer number.
Source: Romania 1997
Tags: number theory proposed, number theory
Suppse that $n\geq 3$ be an inetegr number and $x\in \mathbb{R}$ s.t. $x,x^2$ and $x^n$ have a same decimal representation. Prove that $x$ is an integer number.