$\displaystyle f(x)$ is polynomial with complex coefficients. $\displaystyle \forall n\in Z$, $\displaystyle f(n)$is integer, prove: coefficients of $\displaystyle f(x)$ are rational numbers, and give some examples about rational case.

### Prove:

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* consider coefficients are integers, of course $\displaystyle f(n)$ are integers.

* consider coefficients are rationals, we have $\displaystyle f(x)=\frac{1}{2}x(x+1)$, two consecutive integer can be divided by $\displaystyle 2$, there must be one even number.

How about the cases?:

* real coeffs

* complex coeffs

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And can you give me some more examples?