Solved: Explain why you cannot directly adapt the proof

Chapter 5, Problem 31E

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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,....

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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 ,

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