Explanation (a) a = 4003 , b = − 127 , n = 85 We know a = 4003 = 8 ( mod 85 ) and b = − 127 = 43 ( mod 85 ) . So, a + b = 8 ( mod 85 ) + 43 ( mod 85 ) = 51 ( mod 85 ) a b = 8 ( mod 85 ) .43 ( mod 85 ) = 344 ( mod 85 ) = 4 ( mod 85 ) ( a + b ) 2 = 51 2 ( mod 85 ) = 2601 ( mod 85 ) = 51 ( mod 85 ) (b) a = 17 , 891 , b = 14 , 485 , n = 143 We know a = 17 , 891 = 16 ( mod 143 ) and b = 14 , 485 = 42 ( mod 143 ) . So, a + b = 16 ( mod 143 ) + 42 ( mod 143 ) = 58 ( mod 143 ) a b = 16 ( mod 143 )

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

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Chapter 4.4, Problem 7E

To determine

The value of a+b(modn), ab(modn) and (a+b)2modn in each of the following situations.

a=4003,b=−127,n=85

a=17,891,b=14,485,n=143

a=−389,221,b=123,450,n=10,000

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Chapter 4.4, Problem 6E

Chapter 4.4, Problem 8E

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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. 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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? 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The value of a + b ( mod n ) , a b ( mod n ) and ( a + b ) 2 mod n in each of the following situations. a = 4003 , b = − 127 , n = 85 a = 17 , 891 , b = 14 , 485 , n = 143 a = − 389 , 221 , b = 123 , 450 , n = 10 , 000

Solution Summary: The author explains how to determine the value of a+b(mathrmmodn), ab(

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The value of a+b(modn), ab(modn) and (a+b)2modn in each of the following situations.

a=4003,b=−127,n=85

a=17,891,b=14,485,n=143

a=−389,221,b=123,450,n=10,000

Want to see the full answer?

Chapter 4 Solutions

The value of a + b ( mod n ) , a b ( mod n ) and ( a + b ) 2 mod n in each of the following situations. a = 4003 , b = − 127 , n = 85 a = 17 , 891 , b = 14 , 485 , n = 143 a = − 389 , 221 , b = 123 , 450 , n = 10 , 000

Solution Summary: The author explains how to determine the value of a+b(mathrmmodn), ab(

Concept explainers

Videos

The value of a+b(modn), ab(modn) and (a+b)2modn in each of the following situations. a=4003,b=−127,n=85 a=17,891,b=14,485,n=143 a=−389,221,b=123,450,n=10,000

Want to see the full answer?

Chapter 4 Solutions

The value of a+b(modn), ab(modn) and (a+b)2modn in each of the following situations.

a=4003,b=−127,n=85

a=17,891,b=14,485,n=143

a=−389,221,b=123,450,n=10,000