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
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.