In his article "Polynomials with Integer values" (Resonance), Sury proved an interesting lemma:
If $P$ is a non constant, integral valued, polynomial, then the number of prime divisors of his values $\{P(m)\}_{m\in \mathbb Z}\ $ is infinite, i.e. not all the terms of the sequence $P(0),\ P(1),\ P(2)\ldots $ can be build from finitely many primes.
Does anyone know from where this theorem is taken, or is it a discovery of Sury?