# Can a non-linear polynomial have integers values at only integer points?

P(x) be a polynomial with real co-efficient s,deg(P) greater than or equal to 2.Prove that it is not possible that whenever P(x) is an integer,x is also an integer.

I tried it in various way and I think I have to show that there exists an real number for which P(x) is an integer.

Hint: Find an interval $[n,n+1]$ for which $\left|P(n+1) - P(n)\right| > 1$ where $n$ is an integer (why is this possibile?). Use the intermediate value theorem.