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Math Help - infinite primes?

  1. #1
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    infinite 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?
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  2. #2
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    Suppose there are only finitely many such primes, p_1, p_2, ..., p_n (where p_1=3). Look at the product 4p_2p_3\cdots p_n + 3 and think about what its prime factors must look like.
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  3. #3
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    The case 4k+1 is more difficult.
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