Question

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

Answer 1

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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