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Solved: Adapt the proof in the text that there are
Chapter 4, Problem 55E(choose chapter or problem)
Problem 55E
Adapt the proof in the text that there are infinitely many primes to prove that there are infinitely many primes of the form 4k + 3, where k is a nonnegative integer. [Hint: Suppose that there are only finitely many such primes q1,q2,···,qn, and consider the number 4q1q2···qn – 1.]
Questions & Answers
QUESTION:
Problem 55E
Adapt the proof in the text that there are infinitely many primes to prove that there are infinitely many primes of the form 4k + 3, where k is a nonnegative integer. [Hint: Suppose that there are only finitely many such primes q1,q2,···,qn, and consider the number 4q1q2···qn – 1.]
ANSWER:
Solution
Step 1
Let us suppose that has only finite primes , where j is a non-negative integer
Now, assume that there are n of them
So,
Let us consider now
It is in the form of
Let