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Solved: Adapt the proof in the text that there are

Discrete Mathematics and Its Applications | 7th Edition | ISBN: 9780073383095 | Authors: Kenneth Rosen ISBN: 9780073383095 37

Solution for problem 55E Chapter 4.3

Discrete Mathematics and Its Applications | 7th Edition

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Discrete Mathematics and Its Applications | 7th Edition | ISBN: 9780073383095 | Authors: Kenneth Rosen

Discrete Mathematics and Its Applications | 7th Edition

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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.]

Step-by-Step Solution:

Step 1 </p>

 

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

Step 2 of 2

Chapter 4.3, Problem 55E is Solved
Textbook: Discrete Mathematics and Its Applications
Edition: 7
Author: Kenneth Rosen
ISBN: 9780073383095

This full solution covers the following key subjects: Primes, infinitely, nonnegative, form, hint. This expansive textbook survival guide covers 101 chapters, and 4221 solutions. The full step-by-step solution to problem: 55E from chapter: 4.3 was answered by , our top Math solution expert on 06/21/17, 07:45AM. This textbook survival guide was created for the textbook: Discrete Mathematics and Its Applications, edition: 7. The answer to “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.]” is broken down into a number of easy to follow steps, and 50 words. Since the solution to 55E from 4.3 chapter was answered, more than 266 students have viewed the full step-by-step answer. Discrete Mathematics and Its Applications was written by and is associated to the ISBN: 9780073383095.

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