1.

Show that there areinfinitely many primes of the form 4n+3​

Answer»

All integers are DIVISIBLE by some prime! So every prime which divides N must be of the form 4n+1 (Why must it be of this form?). Because we've assumed that p1,…,PK are the only primes of the form 4n+3. If NONE of those divide N, and 2 doesn't divide N, then all its prime factors must be of the form 4n+1.

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