Explanation As per the division algorithm, let a , b ∈ Z , b ≠ 0 . Then there exists unique integers q and r , with 0 ≤ r < | b | , such that a = q b + r . Now, a = − 15 and b = 4

Discrete Mathematics with Graph Theory (Classic Version) (3rd Edition) (Pearson Modern Classics for Advanced Mathematics Series)

3rd Edition

ISBN: 9780134689555

Author: Edgar Goodaire, Michael Parmenter

Publisher: PEARSON

See similar textbooks

Concept explainers

Transformation of Graphs

The word ‘transformation’ means modification. Transformation of the graph of a function is a process by which we modify or change the original graph and make a new graph.

Exponential Functions

The exponential function is a type of mathematical function which is used in real-world contexts. It helps to find out the exponential decay model or exponential growth model, in mathematical models. In this topic, we will understand descriptive rules, c…

Videos

Question

Chapter 4.1, Problem 5TFQ

To determine

Whether the statement“The equation −15=((−3)×4)+(−3) satisfies the requirements of the Division Algorithm (with a=−15 and b=4).” is true or false.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 4.1, Problem 4TFQ

Chapter 4.1, Problem 6TFQ

Students have asked these similar questions

B) Find 2x -1

Calculate (-3x*-5x²+x-12) + (x + 1) using long division. a. -3x² - 2x-2 remainder -10 b. -3x³-3x²-8x-7 remainder-19 O A B c. -3x³ + 3x² - 8x+9 remainder-21 d. -3x+3x³ - 8x² +9x-21

The figure below shows that 4 one-inch segments are needed to make a 1 × 1 square, 12 one-inch segments are needed to make a 2 × 2 square composed of four 1 × 1 squares, and 24 one-inch segments are needed to make a 3 × 3 square composed of nine 1 × 1 squares. How many one-inch segments are needed to make an nx n square composed of 1 x 1 squares?

Chapter 4 Solutions

Discrete Mathematics with Graph Theory (Classic Version) (3rd Edition) (Pearson Modern Classics for Advanced Mathematics Series)

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

Ch. 4.1 - Prob. 1E Ch. 4.1 - 2. True or false? If false, give a counterexample....Ch. 4.1 - Prob. 3E Ch. 4.1 - Prob. 4E Ch. 4.1 - Prob. 5E Ch. 4.1 - Prob. 6E Ch. 4.1 - Prob. 7E Ch. 4.1 - Prob. 8E Ch. 4.1 - 9. Suppose is a natural number and is the...Ch. 4.1 - Prob. 10E Ch. 4.1 - Prob. 11E Ch. 4.1 - Prob. 12E Ch. 4.2 - True/False Questions Given two consecutive...Ch. 4.2 - Prob. 2TFQ Ch. 4.2 - Prob. 3TFQ Ch. 4.2 - Prob. 4TFQ Ch. 4.2 - Prob. 5TFQ Ch. 4.2 - Prob. 6TFQ Ch. 4.2 - Prob. 7TFQ Ch. 4.2 - Prob. 8TFQ Ch. 4.2 - Prob. 9TFQ Ch. 4.2 - Prob. 10TFQ Ch. 4.2 - Prob. 1E Ch. 4.2 - Prob. 2E Ch. 4.2 - Draw the Hasse diagrams for each of the following...Ch. 4.2 - List all minimal, minimum, maximal, and maximum...Ch. 4.2 - Let n be a natural number. Given n consecutive...Ch. 4.2 - Prove that n22(n an integer) is never divisible by...Ch. 4.2 - Given that a and x are integers, a1, a|(11x+3),...Ch. 4.2 - Prob. 8E Ch. 4.2 - Prob. 9E Ch. 4.2 - Prob. 10E Ch. 4.2 - Prob. 11E Ch. 4.2 - Prob. 12E Ch. 4.2 - Prob. 13E Ch. 4.2 - If a and b are relatively prime integers, prove...Ch. 4.2 - Prob. 15E Ch. 4.2 - Prob. 16E Ch. 4.2 - 17. (a) Find a pair of integers and such that ....Ch. 4.2 - Prob. 18E Ch. 4.2 - Prob. 19E Ch. 4.2 - Prob. 20E Ch. 4.2 - Prob. 21E Ch. 4.2 - If aN, prove that...Ch. 4.2 - Prob. 23E Ch. 4.2 - Prob. 24E Ch. 4.2 - Prob. 25E Ch. 4.2 - Prob. 26E Ch. 4.2 - Prob. 27E Ch. 4.2 - Prob. 28E Ch. 4.2 - Prob. 29E Ch. 4.2 - Prob. 30E Ch. 4.2 - Establish formula (2) of this section by proving...Ch. 4.2 - Prob. 32E Ch. 4.2 - Suppose a,b,c are nonzero integers. Show that...Ch. 4.2 - 34. Suppose that and are partial orders. (a)...Ch. 4.2 - Prob. 35E Ch. 4.2 - Let g be the greatest common divisor of integers m...Ch. 4.3 - 127 is a prime number.Ch. 4.3 - Prob. 2TFQ Ch. 4.3 - Prob. 3TFQ Ch. 4.3 - Prob. 4TFQ Ch. 4.3 - Prob. 5TFQ Ch. 4.3 - Prob. 6TFQ Ch. 4.3 - Prob. 7TFQ Ch. 4.3 - Prob. 8TFQ Ch. 4.3 - Prob. 9TFQ Ch. 4.3 - Prob. 10TFQ Ch. 4.3 - Determine whether each of the following integers...Ch. 4.3 - Prob. 2E Ch. 4.3 - Suppose p is the smallest prime factor of an...Ch. 4.3 - Prob. 4E Ch. 4.3 - Prob. 5E Ch. 4.3 - Prob. 6E Ch. 4.3 - Prob. 7E Ch. 4.3 - Prob. 8E Ch. 4.3 - Prob. 9E Ch. 4.3 - Prob. 10E Ch. 4.3 - Prob. 11E Ch. 4.3 - Prob. 12E Ch. 4.3 - Estimate the number of primes less than 5000, less...Ch. 4.3 - Prob. 14E Ch. 4.3 - Prob. 15E Ch. 4.3 - Prob. 16E Ch. 4.3 - Prob. 17E Ch. 4.3 - 18. (a) Is prime? Explain your answer. (b) Is...Ch. 4.3 - Prob. 19E Ch. 4.3 - Prob. 20E Ch. 4.3 - 21. Show that the sum of two consecutive primes is...Ch. 4.3 - Prob. 22E Ch. 4.3 - Prob. 23E Ch. 4.3 - Prob. 24E Ch. 4.3 - Prob. 25E Ch. 4.3 - Prob. 26E Ch. 4.3 - Let p1p2.......pn+1 denote the first n+1 primes...Ch. 4.3 - Prob. 28E Ch. 4.3 - Prob. 29E Ch. 4.3 - Let a and b be natural numbers. Find the prime...Ch. 4.3 - Prob. 31E Ch. 4.3 - Prob. 32E Ch. 4.3 - 33. Show that there are infinitely many triples of...Ch. 4.3 - Prob. 34E Ch. 4.3 - Prob. 35E Ch. 4.3 - 36. Let denote the set of positive rational...Ch. 4.3 - Prob. 37E Ch. 4.3 - Prob. 38E Ch. 4.4 - A 2003 country music hit by Alan Jackson and Jimmy...Ch. 4.4 - Prob. 2TFQ Ch. 4.4 - Prob. 3TFQ Ch. 4.4 - 4. Ch. 4.4 - Prob. 5TFQ Ch. 4.4 - There are 72 congruence classes of integers mod...Ch. 4.4 - Prob. 7TFQ Ch. 4.4 - Prob. 8TFQ Ch. 4.4 - Prob. 9TFQ Ch. 4.4 - Prob. 10TFQ Ch. 4.4 - Prob. 1E Ch. 4.4 - Prob. 2E Ch. 4.4 - Prob. 3E Ch. 4.4 - 4. True or False? Give a reason for each answer....Ch. 4.4 - Prob. 5E Ch. 4.4 - Prob. 6E Ch. 4.4 - Prob. 7E Ch. 4.4 - Prob. 8E Ch. 4.4 - Find all integers x, 0xn, satisfying each of the...Ch. 4.4 - 10. (a) Given integers and a prime , suppose ....Ch. 4.4 - 11. Find all integers and, , that satisfy each of...Ch. 4.4 - Prob. 12E Ch. 4.4 - Prob. 13E Ch. 4.4 - Prob. 14E Ch. 4.4 - Prob. 15E Ch. 4.4 - Prob. 16E Ch. 4.4 - Prob. 17E Ch. 4.4 - Find all integers x, 0xn, that satisfy each of the...Ch. 4.4 - Find all integers x,0xn, that satisfy each of the...Ch. 4.4 - Find all integers x,0xn, that satisfy each of the...Ch. 4.4 - In each case, find the inverse of a(modn) and use...Ch. 4.4 - In each of the following the given integer p is a...Ch. 4.4 - 23. Show that has no solutions. Ch. 4.4 - 24. Let A be the set of congruence classes of...Ch. 4.5 - Prob. 1TFQ Ch. 4.5 - Prob. 2TFQ Ch. 4.5 - Prob. 3TFQ Ch. 4.5 - Prob. 4TFQ Ch. 4.5 - Prob. 5TFQ Ch. 4.5 - Prob. 6TFQ Ch. 4.5 - Prob. 7TFQ Ch. 4.5 - Prob. 8TFQ Ch. 4.5 - Prob. 9TFQ Ch. 4.5 - Prob. 10TFQ Ch. 4.5 - Prob. 1E Ch. 4.5 - Prob. 2E Ch. 4.5 - Prob. 3E Ch. 4.5 - Prob. 4E Ch. 4.5 - Prob. 5E Ch. 4.5 - Prob. 6E Ch. 4.5 - Prob. 7E Ch. 4.5 - Prob. 8E Ch. 4.5 - Prob. 9E Ch. 4.5 - Prob. 10E Ch. 4.5 - Prob. 11E Ch. 4.5 - Prob. 12E Ch. 4.5 - Prob. 13E Ch. 4.5 - Prob. 14E Ch. 4.5 - Prob. 15E Ch. 4.5 - Prob. 16E Ch. 4.5 - Prob. 17E Ch. 4.5 - 18. In each case, find the smallest nonnegative...Ch. 4.5 - For each of the following, find the smallest...Ch. 4.5 - Prob. 20E Ch. 4.5 - In each of the following cases, find a positive...Ch. 4.5 - Prob. 22E Ch. 4.5 - Prob. 23E Ch. 4.5 - Prob. 24E Ch. 4.5 - 25. Suppose. Decode each of the following encoded...Ch. 4 - Find the quotient and remainder when...Ch. 4 - Convert (1100101)2 to base 10. Convert 32,145 to...Ch. 4 - Prob. 3RE Ch. 4 - An integer n, which has exactly eight factors, is...Ch. 4 - Prob. 5RE Ch. 4 - Prob. 6RE Ch. 4 - Prob. 7RE Ch. 4 - Prob. 8RE Ch. 4 - Illustrate the Euclidean algorithm by showing that...Ch. 4 - Prob. 10RE Ch. 4 - Prob. 11RE Ch. 4 - Prob. 12RE Ch. 4 - 13. Suppose. Show that is not the sum of three...Ch. 4 - Prob. 14RE Ch. 4 - Prob. 15RE Ch. 4 - Prob. 16RE Ch. 4 - Prob. 17RE Ch. 4 - 18. What is the last digit of ? [Hint: You want...Ch. 4 - Prob. 19RE Ch. 4 - Prob. 20RE Ch. 4 - Compute 380(mod7). Find all integers x such that...Ch. 4 - Prob. 22RE Ch. 4 - Prob. 23RE Ch. 4 - Prob. 24RE Ch. 4 - Prob. 25RE Ch. 4 - Prob. 26RE Ch. 4 - Find the smallest positive integer x that...

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.

Whether the statement“The equation − 15 = ( ( − 3 ) × 4 ) + ( − 3 ) satisfies the requirements of the Division Algorithm (with a = − 15 and b = 4 ).” is true or false.

Solution Summary: The author analyzes whether the statement satisfies the requirements of the Division Algorithm.

Concept explainers

Videos

Whether the statement“The equation −15=((−3)×4)+(−3) satisfies the requirements of the Division Algorithm (with a=−15 and b=4).” is true or false.

Want to see the full answer?

Chapter 4 Solutions