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Let f(x) be a monic polynomial of degree n with integer coefficients, and let d1, · · · , dn be pairwise distinct integers. Suppose that for infinitely many prime numbers p there exists an integer kp for which f(kp + d1) ≡ f(kp + d2) ≡ · · · f(kp + dn) ≡ 0 (mod p). Prove that there exists an integer k0 such that f(k0 + d1) = f(k0 + d2) =· · · = f(k0 + dn) = 0