CMO 1970 Problem 10

Given the polynomial $$f(x)=x^n+a_{1}x^{n-1}+a_{2}x^{n-2}+\cdots+a_{n-1}x+a_n$$ with integer coefficients $a_1,a_2,\ldots,a_n$ , and given also that there exist four distinct integers $a$ , $b$ , $c$ and $d$ such that $$f(a)=f(b)=f(c)=f(d)=5,$$ show that there is no integer $k$ such that $f(k)=8$ .