Let $x$ and $y$ be two rational numbers and $n$ be an odd positive integer. Prove that, if $x^n - 2x = y^n - 2y$, then $x = y$.
Source: 2012 Romania JBMO TST 1.2
Tags: algebra, rational, equation
Let $x$ and $y$ be two rational numbers and $n$ be an odd positive integer. Prove that, if $x^n - 2x = y^n - 2y$, then $x = y$.