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What is the proof that for any integer $n$ and any non-constant, integer coefficient polynomial $P(x)$, there are infinitely many primes congruent to $1 \pmod{n}$ that divide $P(x)$ for some $x$?

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    Neglecting the $p \equiv 1 \pmod{n}$ condition, here is a [nice explanation](http://qchu.wordpress.com/2009/09/02/some-remarks-on-the-infinitude-of-primes/) of why there are infinitely many primes dividing $P(x)$ for some $x$.2012-08-21

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