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Solved: Explain why you cannot directly adapt the proof
Chapter 5, Problem 31E(choose chapter or problem)
QUESTION:
Explain why you cannot directly adapt the proof that there are infinitely many primes (Theorem 3 in Section 4.3) to show that are infinitely many primes in the arithmetic progression 4k + 1, k = 1,2,....
Questions & Answers
QUESTION:
Explain why you cannot directly adapt the proof that there are infinitely many primes (Theorem 3 in Section 4.3) to show that are infinitely many primes in the arithmetic progression 4k + 1, k = 1,2,....
ANSWER:Solution:Step 1 :In this problem we have to show that infinitely many primes of the form 4n+1,Suppose there are finitely many primes of the form 4n+1 and they are exactly consider Then for any prime divisor q of N ,