Let $x$ be a real number such that $x ^ { 2014 } - x ^ { 2004 }$ and $x ^ { 2009 } - x ^ { 2004 }$ are both integers. Show that $x$ is an integer. (Hint: it may be useful to first prove that $x$ is rational.)
Let $x$ be a real number such that $x ^ { 2014 } - x ^ { 2004 }$ and $x ^ { 2009 } - x ^ { 2004 }$ are both integers. Show that $x$ is an integer. (Hint: it may be useful to first prove that $x$ is rational.)