Establish that there are infinitely many primes of each of the forms 4k + 1, 6k + 1
Chapter 8, Problem 7(choose chapter or problem)
Establish that there are infinitely many primes of each of the forms 4k + 1, 6k + 1, and8k + 1.[Hint: Assume that there are only finitely many primes of the form 4k + 1; call thempi, p2, ... , Pr Consider the integer (2P1P2 Pr)2 + 1 and apply the previous problem.]
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