In the lecture note of bhatt from arizona winter school 2017, there is an exercise which claims if X is a proper somooth scheme defined over $\mathbb{Z}[1/N]$ and if there is a polynomial $P$ such that for every prime $p$ coprime to $N$ we have $X(F_p)=P(p)$ then the hodge numbers $h^{i,j}=0,i\not =j $

I don't know how to attack this problem because if you want to use zeta functions and weil conjectures you need the number of point of X over all finite fields. But I don't have any counter example. So is there a typo in this exercise or can someone hint how to prove the claim

In the lecture note of Bhatt from Arizona winter school 2017, there is an exercise which claims if X is a proper smooth scheme defined over $\mathbb{Z}[1/N]$ and if there is a polynomial $P$ such that for every prime $p$ coprime to $N$ we have $X(F_p)=P(p)$ then the Hodge numbers $h^{i,j}=0,i\not =j $

I do not know how to attack this problem because if you want to use zeta functions and Weil conjectures you need the number of points of X over all finite fields. But I do not have any counter example. So is there a typo in this exercise or can someone hint how to prove the claim ?