How do you prove that there exists infinitely many primes p such that p = 2 mod 3 ?

I know that we can use the Euclid's Theorem but I have no idea how to do this kind of question, can anyone give me some hints?

Thanks alot

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- October 2nd 2008, 06:47 AMknguyen2005Euclid's Theorem
How do you prove that there exists infinitely many primes p such that p = 2 mod 3 ?

I know that we can use the Euclid's Theorem but I have no idea how to do this kind of question, can anyone give me some hints?

Thanks alot - October 2nd 2008, 07:58 AMThePerfectHacker
Assume there are finitely many .

Form .

We know that has an odd prime divisor . If all its prime divisiors were of the form then would be of the form and impossibility. Therefore there is a prime divisor of the form . Thus, and it must be amongst . But that leads to which is a contradiction. - October 2nd 2008, 11:52 AMknguyen2005
thank you very much ThePerfectHacker