hello guys . question here

how can i prove that there exists infinitely many primes p such that p = 3 mod 4.

i have a little inkling as i know that if a,b=1 mod 4 then ab = 1 mod 4. Im guessing it would be along the lines of euclids theorem?

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- Oct 12th 2007, 01:28 PMjoanne_qinfinite primes?
hello guys . question here

how can i prove that there exists infinitely many primes p such that p = 3 mod 4.

i have a little inkling as i know that if a,b=1 mod 4 then ab = 1 mod 4. Im guessing it would be along the lines of euclids theorem? - Oct 13th 2007, 12:05 AMOpalg
Suppose there are only finitely many such primes, p_1, p_2, ..., p_n (where p_1=3). Look at the product $\displaystyle 4p_2p_3\cdots p_n + 3$ and think about what its prime factors must look like.

- Oct 13th 2007, 04:42 PMThePerfectHacker
The case 4k+1 is more difficult.