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Contemporary Abstract Algebra

9th Edition

Joseph Gallian

Publisher: Cengage Learning

ISBN: 9781305657960

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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 22E:

Express (73i)1 in standard form.

Problem 23E:

Express 5+2i45i in standard form.

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 31E:

Use the Generalized Euclid’s Lemma (see Exercise 30) to establish the uniqueness portion of the...

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 52E:

The ISBN-10 0669039254 is the result of a transposition of two adjacent digits not involving the...

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?

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

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

For n=5 , 8, 12, 20, and 25, find all positive integers less than n and relatively prime to n.With pictures and words, describe each symmetry in D3 (the set of symmetries of an equilateral...Which of the following binary operations are closed? a. subtraction of positive integers b. division...For each group in the following list, find the order of the group and the order of each element in...Find all generators of Z6,Z8,andZ20 .Let [123456213546]and=[123456612435] . Compute each of the following. a. 1 b. c.Being a mathematician is a bit like being a manic depressive: you spend yourlife alternating between...Let H=0,3,6,9,... . Find all the left cosets of H in Z.

Corresponding editions of this textbook are also available below:

Contemporary Abstract Algebra.

6 Edition

ISBN: 9780618514717

EBK CONTEMPORARY ABSTRACT ALGEBRA

8 Edition

ISBN: 9780100453074

Contemporary Abstract Algebra

8 Edition

ISBN: 9781133599708

Contemporary Abstract Algebra

8 Edition

ISBN: 9781285402734

Contemporary Abstract Algebra

8 Edition

ISBN: 9788131520741

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

8 Edition

ISBN: 9781133608530

EBK CONTEMPORARY ABSTRACT ALGEBRA

8 Edition

ISBN: 8220100453076

Contemporary Abstract Algebra, 7th Edition

7 Edition

ISBN: 9780547165097

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

7 Edition

ISBN: 9780547165394

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

9 Edition

ISBN: 9781305657977

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

9 Edition

ISBN: 9781337501590

EBK CONTEMPORARY ABSTRACT ALGEBRA

9 Edition

ISBN: 8220101434852

EBK CONTEMPORARY ABSTRACT ALGEBRA

9 Edition

ISBN: 9781305887855

Contemporary Abstract Algebra

5 Edition

ISBN: 9780618122141

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