Let:

$P=P(x)=a_nx^n+a_{n-1}x^{n-1}+\ldots+a_0\in{\mathbb Z}[x]$

...be a polynomial with $a_0\not=0$ and $a_n\not=0$.

Let $r$, $s$ be integers with greatest common divisor equal $1$ and suppose $P(r/s)=0$.

Which of the following is *always* true?