Let n be a positive integer not less than 4. Show that there exists a polynomial with integral coefficients f(x)=xn+an−1xn−1+an−2xn−2+⋯+a1x+a0
such that for any positive integer m and any k≥2 distinct integers r1, r2, ⋯, rk, it always hold that f(m)≠f(r1)f(r2)⋯f(rk).