Question 192
In an infinite sequence $\{\alpha\}$, $\{\alpha^2\}$, $\{\alpha^3\}$, ... there are only finitely many distinct values. Show that $\alpha$ is an integer. ($\{x\}$ denotes the fractional part of $x$, i.e. $\{x\} = x - [x]$, where $[x]$ is the greatest integer not greater than $x$.) (Golovanov A.S.)