Given the polynomial f(x)=xn+a1xn−1+a2xn−2+⋯+an−1x+an with integer coefficients a1,a2,…,an, 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.