Explanation Given information: Let N = 2 ⋅ 3 ⋅ 5 ⋅ 7 + 1 . What remainder is obtained when N is divided by 2 ? 3 ? 5 ? 7 ? Is N prime? Justify your answer. Calculation: The given information states that the value of N integer is N = 2 ⋅ 3 ⋅ 5 ⋅ 7 + 1 = 211 . If a divides b if there exists an integer c such that b = a c notations: a | b Quotient-Remainder theorem: Let n be an integer and d is a positive integer. Then there are unique integers q and r with 0 ≤ r < d such that n = d q + r . N is not divisible by 2 , because N 2 = 2 ⋅ 3 ⋅ 5 ⋅ 7 + 1 2 = 3 ⋅ 5 ⋅ 7 + 1 2 is not an integer since 1 2 is not an integer. N is not divisible by 3 , because N 3 = 2 ⋅ 3 ⋅ 5 ⋅ 7 + 1 3 = 2 ⋅ 5 ⋅ 7 + 1 3 is not an integer since 1 3 is not an integer. N is not divisible by 5 , because N 5 = 2 ⋅ 3 ⋅ 5 ⋅ 7 + 1 5 = 2 ⋅ 3 ⋅ 7 + 1 5 is not an integer since 1 5 is not an integer

Discrete Mathematics: Introduction to Mathematical Reasoning

1st Edition

ISBN: 9780495826170

Author: Susanna S. Epp

Publisher: Cengage Learning

See similar textbooks

Concept explainers

Set Theory

Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.

Question

Chapter 4.6, Problem 25ES

To determine

To prove: The irrational number by the proof technique.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 4.6, Problem 24ES

Chapter 4.6, Problem 26ES

Students have asked these similar questions

Homework Let X1, X2, Xn be a random sample from f(x;0) where f(x; 0) = (-), 0 < x < ∞,0 € R Using Basu's theorem, show that Y = min{X} and Z =Σ(XY) are indep. -

Homework Let X1, X2, Xn be a random sample from f(x; 0) where f(x; 0) = e−(2-0), 0 < x < ∞,0 € R Using Basu's theorem, show that Y = min{X} and Z =Σ(XY) are indep.

rmine the immediate settlement for points A and B shown in figure below knowing that Aq,-200kN/m², E-20000kN/m², u=0.5, Depth of foundation (DF-0), thickness of layer below footing (H)=20m. 4m B 2m 2m A 2m + 2m 4m

Chapter 4 Solutions

Discrete Mathematics: Introduction to Mathematical Reasoning

Ch. 4.1 - Prob. 1ES Ch. 4.1 - Prob. 2ES Ch. 4.1 - Prob. 3ES Ch. 4.1 - Prob. 4ES Ch. 4.1 - Prob. 5ES Ch. 4.1 - Prob. 6ES Ch. 4.1 - Prob. 7ES Ch. 4.1 - Prob. 8ES Ch. 4.1 - Prob. 9ES Ch. 4.1 - Prob. 10ES

Ch. 4.1 - Prob. 11ES Ch. 4.1 - Prob. 12ES Ch. 4.1 - Prob. 13ES Ch. 4.1 - Prob. 14ES Ch. 4.1 - Prob. 15ES Ch. 4.1 - Prob. 16ES Ch. 4.1 - Prob. 17ES Ch. 4.1 - Prob. 18ES Ch. 4.1 - Prob. 19ES Ch. 4.1 - Prob. 20ES Ch. 4.1 - Prob. 21ES Ch. 4.1 - Prob. 22ES Ch. 4.1 - Prob. 23ES Ch. 4.1 - Prob. 24ES Ch. 4.1 - Prob. 25ES Ch. 4.1 - Prob. 26ES Ch. 4.1 - Prob. 27ES Ch. 4.1 - Prob. 28ES Ch. 4.1 - Prob. 29ES Ch. 4.1 - Prob. 30ES Ch. 4.1 - Prob. 31ES Ch. 4.1 - Prob. 32ES Ch. 4.1 - Prob. 33ES Ch. 4.1 - Prob. 34ES Ch. 4.1 - Prob. 35ES Ch. 4.1 - Prob. 36ES Ch. 4.1 - Prob. 37ES Ch. 4.1 - Prob. 38ES Ch. 4.1 - Prob. 39ES Ch. 4.1 - Prob. 40ES Ch. 4.1 - Prob. 41ES Ch. 4.1 - Prob. 42ES Ch. 4.1 - Prob. 43ES Ch. 4.1 - Prob. 44ES Ch. 4.1 - Prob. 45ES Ch. 4.1 - Prob. 46ES Ch. 4.1 - Prob. 47ES Ch. 4.1 - Prob. 48ES Ch. 4.1 - Prob. 49ES Ch. 4.1 - Prob. 50ES Ch. 4.1 - Prob. 51ES Ch. 4.1 - Prob. 52ES Ch. 4.1 - Prob. 53ES Ch. 4.1 - Prob. 54ES Ch. 4.1 - Prob. 55ES Ch. 4.1 - Prob. 56ES Ch. 4.1 - Prob. 57ES Ch. 4.1 - Prob. 58ES Ch. 4.1 - Prob. 59ES Ch. 4.1 - Prob. 60ES Ch. 4.1 - Prob. 61ES Ch. 4.1 - Prob. 62ES Ch. 4.1 - Prob. 63ES Ch. 4.2 - Prob. 1ES Ch. 4.2 - Prob. 2ES Ch. 4.2 - Prob. 3ES Ch. 4.2 - Prob. 4ES Ch. 4.2 - Prob. 5ES Ch. 4.2 - Prob. 6ES Ch. 4.2 - Prob. 7ES Ch. 4.2 - Prob. 8ES Ch. 4.2 - Prob. 9ES Ch. 4.2 - Prob. 10ES Ch. 4.2 - Prob. 11ES Ch. 4.2 - Prob. 12ES Ch. 4.2 - Prob. 13ES Ch. 4.2 - Prob. 14ES Ch. 4.2 - Prob. 15ES Ch. 4.2 - Prob. 16ES Ch. 4.2 - Prob. 17ES Ch. 4.2 - Prob. 18ES Ch. 4.2 - Prob. 19ES Ch. 4.2 - Prob. 20ES Ch. 4.2 - Prob. 21ES Ch. 4.2 - Prob. 22ES Ch. 4.2 - Prob. 23ES Ch. 4.2 - Prob. 24ES Ch. 4.2 - Prob. 25ES Ch. 4.2 - Prob. 26ES Ch. 4.2 - Prob. 27ES Ch. 4.2 - Prob. 28ES Ch. 4.2 - Prob. 29ES Ch. 4.2 - Prob. 30ES Ch. 4.2 - Prob. 31ES Ch. 4.2 - Prob. 32ES Ch. 4.2 - Prob. 33ES Ch. 4.2 - Prob. 34ES Ch. 4.2 - Prob. 35ES Ch. 4.2 - Prob. 36ES Ch. 4.2 - Prob. 37ES Ch. 4.2 - Prob. 38ES Ch. 4.2 - Prob. 39ES Ch. 4.3 - Prob. 1ES Ch. 4.3 - Prob. 2ES Ch. 4.3 - Prob. 3ES Ch. 4.3 - Prob. 4ES Ch. 4.3 - Prob. 5ES Ch. 4.3 - Prob. 6ES Ch. 4.3 - Prob. 7ES Ch. 4.3 - Prob. 8ES Ch. 4.3 - Prob. 9ES Ch. 4.3 - Prob. 10ES Ch. 4.3 - Prob. 11ES Ch. 4.3 - Prob. 12ES Ch. 4.3 - Prob. 13ES Ch. 4.3 - Prob. 14ES Ch. 4.3 - Prob. 15ES Ch. 4.3 - Prob. 16ES Ch. 4.3 - Prob. 17ES Ch. 4.3 - Prob. 18ES Ch. 4.3 - Prob. 19ES Ch. 4.3 - Prob. 20ES Ch. 4.3 - Prob. 21ES Ch. 4.3 - Prob. 22ES Ch. 4.3 - Prob. 23ES Ch. 4.3 - Prob. 24ES Ch. 4.3 - Prob. 25ES Ch. 4.3 - Prob. 26ES Ch. 4.3 - Prob. 27ES Ch. 4.3 - Prob. 28ES Ch. 4.3 - Prob. 29ES Ch. 4.3 - Prob. 30ES Ch. 4.3 - Prob. 31ES Ch. 4.3 - Prob. 32ES Ch. 4.3 - Prob. 33ES Ch. 4.3 - Prob. 34ES Ch. 4.3 - Prob. 35ES Ch. 4.3 - Prob. 36ES Ch. 4.3 - Prob. 37ES Ch. 4.3 - Prob. 38ES Ch. 4.3 - Prob. 39ES Ch. 4.3 - Prob. 40ES Ch. 4.3 - Prob. 41ES Ch. 4.3 - Prob. 42ES Ch. 4.3 - Prob. 43ES Ch. 4.3 - Prob. 44ES Ch. 4.3 - Prob. 45ES Ch. 4.3 - Prob. 46ES Ch. 4.3 - Prob. 47ES Ch. 4.3 - Prob. 48ES Ch. 4.3 - Prob. 49ES Ch. 4.4 - Prob. 1ES Ch. 4.4 - Prob. 2ES Ch. 4.4 - Prob. 3ES Ch. 4.4 - Prob. 4ES Ch. 4.4 - Prob. 5ES Ch. 4.4 - Prob. 6ES Ch. 4.4 - Prob. 7ES Ch. 4.4 - Prob. 8ES Ch. 4.4 - Prob. 9ES Ch. 4.4 - Prob. 10ES Ch. 4.4 - Prob. 11ES Ch. 4.4 - Prob. 12ES Ch. 4.4 - Prob. 13ES Ch. 4.4 - Prob. 14ES Ch. 4.4 - Prob. 15ES Ch. 4.4 - Prob. 16ES Ch. 4.4 - Prob. 17ES Ch. 4.4 - Prob. 18ES Ch. 4.4 - Prob. 19ES Ch. 4.4 - Prob. 20ES Ch. 4.4 - Prob. 21ES Ch. 4.4 - Prob. 22ES Ch. 4.4 - Prob. 23ES Ch. 4.4 - Prob. 24ES Ch. 4.4 - Prob. 25ES Ch. 4.4 - Prob. 26ES Ch. 4.4 - Prob. 27ES Ch. 4.4 - Prob. 28ES Ch. 4.4 - Prob. 29ES Ch. 4.4 - Prob. 30ES Ch. 4.4 - Prob. 31ES Ch. 4.4 - Prob. 32ES Ch. 4.4 - Prob. 33ES Ch. 4.4 - Prob. 34ES Ch. 4.4 - Prob. 35ES Ch. 4.4 - Prob. 36ES Ch. 4.4 - Prob. 37ES Ch. 4.4 - Prob. 38ES Ch. 4.4 - Prob. 39ES Ch. 4.4 - Prob. 40ES Ch. 4.4 - Prob. 41ES Ch. 4.4 - Prob. 42ES Ch. 4.4 - Prob. 43ES Ch. 4.4 - Prob. 44ES Ch. 4.4 - Prob. 45ES Ch. 4.4 - Prob. 46ES Ch. 4.5 - Prob. 1ES Ch. 4.5 - Prob. 2ES Ch. 4.5 - Prob. 3ES Ch. 4.5 - Prob. 4ES Ch. 4.5 - Prob. 5ES Ch. 4.5 - Prob. 6ES Ch. 4.5 - Prob. 7ES Ch. 4.5 - Prob. 8ES Ch. 4.5 - Prob. 9ES Ch. 4.5 - Prob. 10ES Ch. 4.5 - Prob. 11ES Ch. 4.5 - Prob. 12ES Ch. 4.5 - Prob. 13ES Ch. 4.5 - Prob. 14ES Ch. 4.5 - Prob. 15ES Ch. 4.5 - Prob. 16ES Ch. 4.5 - Prob. 17ES Ch. 4.5 - Prob. 18ES Ch. 4.5 - Prob. 19ES Ch. 4.5 - Prob. 20ES Ch. 4.5 - Prob. 21ES Ch. 4.5 - Prob. 22ES Ch. 4.5 - Prob. 23ES Ch. 4.5 - Prob. 24ES Ch. 4.5 - Prob. 25ES Ch. 4.5 - Prob. 26ES Ch. 4.5 - Prob. 27ES Ch. 4.5 - Prob. 28ES Ch. 4.5 - Prob. 29ES Ch. 4.5 - Prob. 30ES Ch. 4.5 - Prob. 31ES Ch. 4.5 - Prob. 32ES Ch. 4.5 - Prob. 33ES Ch. 4.5 - Prob. 34ES Ch. 4.5 - Prob. 35ES Ch. 4.6 - Prob. 1ES Ch. 4.6 - Prob. 2ES Ch. 4.6 - Prob. 3ES Ch. 4.6 - Prob. 4ES Ch. 4.6 - Prob. 5ES Ch. 4.6 - Prob. 6ES Ch. 4.6 - Prob. 7ES Ch. 4.6 - Prob. 8ES Ch. 4.6 - Prob. 9ES Ch. 4.6 - Prob. 10ES Ch. 4.6 - Prob. 11ES Ch. 4.6 - Prob. 12ES Ch. 4.6 - Prob. 13ES Ch. 4.6 - Prob. 14ES Ch. 4.6 - Prob. 15ES Ch. 4.6 - Prob. 16ES Ch. 4.6 - Prob. 17ES Ch. 4.6 - Prob. 18ES Ch. 4.6 - Prob. 19ES Ch. 4.6 - Prob. 20ES Ch. 4.6 - Prob. 21ES Ch. 4.6 - Prob. 22ES Ch. 4.6 - Prob. 23ES Ch. 4.6 - Prob. 24ES Ch. 4.6 - Prob. 25ES Ch. 4.6 - Prob. 26ES Ch. 4.6 - Prob. 27ES Ch. 4.6 - Prob. 28ES Ch. 4.6 - Prob. 29ES Ch. 4.6 - Prob. 30ES Ch. 4.6 - Prob. 31ES Ch. 4.6 - Prob. 32ES Ch. 4.6 - Prob. 33ES Ch. 4.6 - Prob. 34ES Ch. 4.6 - Prob. 35ES

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.

To prove: The irrational number by the proof technique.

Solution Summary: The author explains the irrational number by the proof technique. The value of N is not divisible by 2.

Concept explainers

To prove: The irrational number by the proof technique.

Want to see the full answer?

Chapter 4 Solutions