## Solutions for Contemporary Abstract Algebra

Problem 1E:

For n=5 , 8, 12, 20, and 25, find all positive integers less than n and relatively prime to n.Problem 2E:

Determine a. gcd(2,10) lcm(2,10) b. gcd(20,8) lcm(20,8) d. gcd(21,50) lcm(21,50) e. gcd (p2q2,pq3)...Problem 3E:

Determine 51 mod 13, 342 mod 85, 62 mod 15, 10 mod 15, (8273) mod 7, (51+68) mod 7, (3524) mod 11,...Problem 6E:

Suppose a and b are integers that divide the integer c. If a and b are relatively prime, show that...Problem 7E:

If a and b are integers and n is a positive integer, prove that a mod n=b mod n if and only if n...Problem 9E:

Let n be a fixed positive integer greater than 1. If a mod n=a and b mod n=b , prove that...Problem 10E:

Let a and b be positive integers and let d=gcd(a,b) and m=lcm(a,b) . If t divides both a and b,...Problem 11E:

Let n and a be positive integers and let d=gcd(a,n) . Show that the equation ax mod n=1 has a...Problem 13E:

Suppose that m and n are relatively prime and r is any integer. Showthat there are integers x and y...Problem 16E:

Determine 71000 mod 6 and 61001 mod 7.Problem 17E:

Let a, b, s, and t be integers. If a mod st=bmodst, show that amod s=bmods and a mod t=bmodt. What...Problem 18E:

Determine 8402 mod 5.Problem 19E:

Show that gcd(a,bc)=1 if and only if gcd(a,b)=1 and gcd(a,c)=1 . (This exercise is referred to in...Problem 25E:

Give an “if and only if” statement that describes when the logic gatex NAND y modeled by 1+xy is 1....Problem 26E:

For inputs of 0 and 1 and mod 2 arithmetic describe the output ofthe formula z+xy+xz in the form “If...Problem 27E:

For every positive integer n, prove that a set with exactly n elements has exactly 2n subsets...Problem 28E:

Prove that 2n32n1 is always divisible by 17.Problem 29E:

Prove that there is some positive integer n such that n, n+1,n+2, , n+200 are all composite.Problem 30E:

(Generalized Euclid’s Lemma) If p is a prime and p divides a1a2an , prove that p divides ai for some...Problem 32E:

What is the largest bet that cannot be made with chips worth $7.00 and $9.00? Verify that your...Problem 33E:

Prove that the First Principle of Mathematical Induction is a consequence of the Well Ordering...Problem 34E:

The Fibonacci numbers are 1, 1, 2, 3, 5, 8, 13, 21, 34, . . . . In general,the Fibonacci numbers are...Problem 35E:

Prove by induction on n that for all positive integers n, n3+(n+1)3+(n+2)3 is a multiple of 9.Problem 36E:

Suppose that there is a statement involving a positive integer parameter n and you have an argument...Problem 37E:

In the cut “As” from Songs in the Key of Life, Stevie Wonder mentions the equation 888=4 . Find all...Problem 38E:

Prove that for every integer n, n3 mod 6=n mod 6.Problem 41E:

Suppose that in one of the noncheck positions of a money order number, the digit 0 is substituted...Problem 42E:

Suppose that a money order identification number and check digit of 21720421168 is erroneously...Problem 43E:

A transposition error involving distinct adjacent digits is one of theform ...ab......ba... with ab...Problem 44E:

Determine the check digit for the Avis rental car with identification number 540047. (See Example...Problem 45E:

Show that a substitution of a digit ai for the digit ai(aiai) in a noncheck position of a UPS number...Problem 46E:

Determine which transposition errors involving adjacent digits are detected by the UPS check digit.Problem 48E:

Explain why the check digit for a money order for the number N is the repeated decimal digit in the...Problem 49E:

The 10-digit International Standard Book Number (ISBN-10) a1a2a3a4a5a6a7a8a9a10 has the property...Problem 50E:

Suppose that an ISBN-10 has a smudged entry where the question mark appears in the number 0716?28419...Problem 51E:

Suppose three consecutive digits abc of an ISBN-10 are scrambled as bca. Which such errors will go...Problem 53E:

Suppose the weighting vector for ISBN-10s were changed to (1, 2,3, 4, 5, 6, 7, 8, 9, 10). Explain...Problem 54E:

Use the two-check-digit error-correction method described in thischapter to append two check digits...Problem 55E:

Suppose that an eight-digit number has two check digits appended using the error-correction method...Problem 56E:

The state of Utah appends a ninth digit a9 to an eight-digit driver’slicense number a1a2...a8 so...Problem 57E:

Complete the proof of Theorem 0.8.Problem 58E:

Let S be the set of real numbers. If a,bS , define a~b if ab isan integer. Show that ~is an...Problem 59E:

Let S be the set of integers. If a,bS , define aRb if ab0 . Is R an equivalence relation on S?# Browse All Chapters of This Textbook

Chapter 0 - PreliminariesChapter 1 - Introduction To GroupsChapter 2 - GroupsChapter 3 - Finite Groups; SubgroupsChapter 4 - Cyclic GroupsChapter 5 - Permutation GroupsChapter 6 - IsomorphismsChapter 7 - Cosets And Lagrange’s TheoremChapter 9 - Normal Subgroups And Factor GroupsChapter 10 - Group Homomorphisms

Chapter 12 - Introduction To RingsChapter 13 - Integral DomainsChapter 14 - Ideals And Factor RingsChapter 18 - Divisibility In Integral DomainsChapter 20 - Extension FieldsChapter 26 - Generators And RelationsChapter 28 - Frieze Groups And Crystallographic GroupsChapter 30 - Cayley Digraphs Of Groups

# Sample Solutions for this Textbook

We offer sample solutions for Contemporary Abstract Algebra homework problems. See examples below:

Chapter 0, Problem 1EGiven: An equilateral triangle. Calculation: Three rotations at 0, 120 and 240 gives the symmetric...Chapter 2, Problem 1EChapter 3, Problem 1EChapter 4, Problem 1EChapter 5, Problem 1EGiven information: Concept used: Isomorphism: - A homomorphism ϕ from G into G¯ is said to be an...Chapter 7, Problem 1EChapter 9, Problem 1E

# More Editions of This Book

Corresponding editions of this textbook are also available below:

Contemporary Abstract Algebra.

6th Edition

ISBN: 9780618514717

EBK CONTEMPORARY ABSTRACT ALGEBRA

8th Edition

ISBN: 9780100453074

Contemporary Abstract Algebra

8th Edition

ISBN: 9781133599708

Contemporary Abstract Algebra

8th Edition

ISBN: 9781285402734

Contemporary Abstract Algebra

8th Edition

ISBN: 9788131520741

Student Solutions Manual For Gallian's Contemporary Abstract Algebra, 8th

8th Edition

ISBN: 9781133608530

EBK CONTEMPORARY ABSTRACT ALGEBRA

8th Edition

ISBN: 8220100453076

Contemporary Abstract Algebra, 7th Edition

7th Edition

ISBN: 9780547165097

Student Solutions Manual For Gallian's Contemporary Abstract Algebra, 7th (students Solutions Manual)

7th Edition

ISBN: 9780547165394

Student Solutions Manual for Gallian's Contemporary Abstract Algebra, 9th

9th Edition

ISBN: 9781305657977

Bundle: Contemporary Abstract Algebra, 9th + Student Solutions Manual

9th Edition

ISBN: 9781337501590

EBK CONTEMPORARY ABSTRACT ALGEBRA

9th Edition

ISBN: 8220101434852

EBK CONTEMPORARY ABSTRACT ALGEBRA

9th Edition

ISBN: 9781305887855

Contemporary Abstract Algebra

9th Edition

ISBN: 9781337249560

Contemporary Abstract Algebra

5th Edition

ISBN: 9780618122141

Contemporary Abstract Algebra

10th Edition

ISBN: 9781000337358

CONTEMPORARY ABSTRACT ALGEBRA

10th Edition

ISBN: 9780367651787

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