1970 Canadian MO Problems/Problem 10

Problem

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 $f(k)=8$ .

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1970 Canadian MO Problems/Problem 10

Problem

Solution