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Dec 2, 2013 at 17:04 comment added Peter Mueller O.K., Qiaochu Yuan's elegant and elementary answer does what you want.
Dec 2, 2013 at 15:34 comment added l.t Thank you. Indeed, I forgot about Gauss Lemma, so I feel silly asking about $\mathbb{Q}[X]$ now. However, Hilbert's Theorem is too advanced for me, unless there is a simple proof for this case. I was thinking to look for big primes, but I haven't found anything useful yet.
S Dec 2, 2013 at 15:28 history answered Peter Mueller CC BY-SA 3.0
S Dec 2, 2013 at 15:28 history made wiki Post Made Community Wiki by Peter Mueller