algebra precalculus - prove that there is no k such that $x^2-x+k$ divides $x^{135}+x+2016$

how would you prove that there exists no $k \in \Bbb{N}$ such that for all
$x\in\Bbb{Z}$ the integer $x^2-x+k$ divides $x^{135}+x+2016$? I started off with contradiction by assuming that there exists a k such that $x^2-x+k$ divides $x^{135}+x+2016$
then $(x^2-x+k)r=x^{135}+x+2016$ for some $r \in \Bbb{Z}$ but from this point im finding it really hard to draw a contradiction.