To prove: That every odd positive integer of the form 3 n + 2 , n ∈ N , has a prime factor of the same form. What happens if the word odd is omitted?

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Answer 1

Question

Chapter 4.3, Problem 34E

(a)

To determine

To prove: That every odd positive integer of the form 3n+2,n∈N, has a prime factor of the same form. What happens if the word odd is omitted?

(b)

To determine

To prove: That every odd positive integer of the form 4n+3,n∈N, has a prime factor of the same form. What happens if the word odd is omitted?

(c)

To determine

To prove: That every odd positive integer of the form 6n+5,n∈N, has a prime factor of the same form. What happens if the word odd is omitted?

(d)

To determine

To prove: That there are infinitely many primes of the form 6n+5.

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Answer 2

Question

Chapter 4.3, Problem 34E

(a)

To determine

To prove: That every odd positive integer of the form 3n+2,n∈N, has a prime factor of the same form. What happens if the word odd is omitted?

(b)

To determine

To prove: That every odd positive integer of the form 4n+3,n∈N, has a prime factor of the same form. What happens if the word odd is omitted?

(c)

To determine

To prove: That every odd positive integer of the form 6n+5,n∈N, has a prime factor of the same form. What happens if the word odd is omitted?

(d)

To determine

To prove: That there are infinitely many primes of the form 6n+5.

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Answer 3

Question

Chapter 4.3, Problem 34E

(a)

To determine

To prove: That every odd positive integer of the form 3n+2,n∈N, has a prime factor of the same form. What happens if the word odd is omitted?

(b)

To determine

To prove: That every odd positive integer of the form 4n+3,n∈N, has a prime factor of the same form. What happens if the word odd is omitted?

(c)

To determine

To prove: That every odd positive integer of the form 6n+5,n∈N, has a prime factor of the same form. What happens if the word odd is omitted?

(d)

To determine

To prove: That there are infinitely many primes of the form 6n+5.

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Answer 4

Question

Chapter 4.3, Problem 34E

(a)

To determine

To prove: That every odd positive integer of the form 3n+2,n∈N, has a prime factor of the same form. What happens if the word odd is omitted?

(b)

To determine

To prove: That every odd positive integer of the form 4n+3,n∈N, has a prime factor of the same form. What happens if the word odd is omitted?

(c)

To determine

To prove: That every odd positive integer of the form 6n+5,n∈N, has a prime factor of the same form. What happens if the word odd is omitted?

(d)

To determine

To prove: That there are infinitely many primes of the form 6n+5.

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Answer 5

Chapter 4.3, Problem 34E

(a)

To determine

To prove: That every odd positive integer of the form 3n+2,n∈N, has a prime factor of the same form. What happens if the word odd is omitted?

(b)

To determine

To prove: That every odd positive integer of the form 4n+3,n∈N, has a prime factor of the same form. What happens if the word odd is omitted?

(c)

To determine

To prove: That every odd positive integer of the form 6n+5,n∈N, has a prime factor of the same form. What happens if the word odd is omitted?

(d)

To determine

To prove: That there are infinitely many primes of the form 6n+5.

Answer 6

Chapter 4.3, Problem 34E

(a)

To determine

To prove: That every odd positive integer of the form 3n+2,n∈N, has a prime factor of the same form. What happens if the word odd is omitted?

Answer 7

Chapter 4.3, Problem 34E

(a)

To determine

To prove: That every odd positive integer of the form 3n+2,n∈N, has a prime factor of the same form. What happens if the word odd is omitted?

Answer 8

(b)

To determine

To prove: That every odd positive integer of the form 4n+3,n∈N, has a prime factor of the same form. What happens if the word odd is omitted?

Answer 9

(b)

To determine

To prove: That every odd positive integer of the form 4n+3,n∈N, has a prime factor of the same form. What happens if the word odd is omitted?

Answer 10

(c)

To determine

To prove: That every odd positive integer of the form 6n+5,n∈N, has a prime factor of the same form. What happens if the word odd is omitted?

Answer 11

(c)

To determine

To prove: That every odd positive integer of the form 6n+5,n∈N, has a prime factor of the same form. What happens if the word odd is omitted?

Answer 12

(d)

To determine

To prove: That there are infinitely many primes of the form 6n+5.

Answer 13

(d)

To determine

To prove: That there are infinitely many primes of the form 6n+5.

Answer 14

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Answer 15

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Answer 16

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Answer 17

Ch. 4.1 - 227 Ch. 4.1 - The Well-Ordering Principle states that any...Ch. 4.1 - Prob. 3TFQ Ch. 4.1 - Prob. 4TFQ Ch. 4.1 - Prob. 5TFQ Ch. 4.1 - Prob. 6TFQ Ch. 4.1 - Prob. 7TFQ Ch. 4.1 - Prob. 8TFQ Ch. 4.1 - Prob. 9TFQ Ch. 4.1 - Prob. 10TFQ

To prove: That every odd positive integer of the form 3 n + 2 , n ∈ N , has a prime factor of the same form. What happens if the word odd is omitted?

Solution Summary: The author explains that every odd positive integer of the form 3n+2,nin N, has a prime factor.

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To prove: That every odd positive integer of the form 3n+2,n∈N, has a prime factor of the same form. What happens if the word odd is omitted?

To prove: That every odd positive integer of the form 4n+3,n∈N, has a prime factor of the same form. What happens if the word odd is omitted?

To prove: That every odd positive integer of the form 6n+5,n∈N, has a prime factor of the same form. What happens if the word odd is omitted?

To prove: That there are infinitely many primes of the form 6n+5.

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Chapter 4 Solutions