Logo
Home Study Material Contact Search
AI Chat FREE
  1. mathematics
  2. advance math
  3. a) suppose that a ? z is a unit modulo n. prove th

a) Suppose that a ? Z is a unit modulo n. Prove that its inverse modulo...

70.2K

Verified Solution

Question

Advance Math

a) Suppose that a ? Z is a unit modulo n. Prove that its inversemodulo n is well defined as a residue class in Zn, and depends onlyon the residue class a in Zn.

b) Let Z × n ? Zn be the set of invertible residue classesmodulo n. Prove that Z × n forms a group under multiplication. Isthis group a subgroup of Zn?

c) List the elements of Z × 9 . How many are there? For eachresidue class u ? Z9, compute the elements of the sequence u, u2 ,u3 , u4 , . . . until the pattern is clear. Determine the length ofeach repeating cycle. Is Z × 9 a cyclic group?

Answer & Explanation Solved by verified expert
3.7 Ratings (297 Votes)
    See Answer
Get Answers to Unlimited Questions

Join us to gain access to millions of questions and expert answers. Enjoy exclusive benefits tailored just for you!

Membership Benefits:
  • Unlimited Question Access with detailed Answers
  • Zin AI - 3 Million Words
  • 10 Dall-E 3 Images
  • 20 Plot Generations
  • Conversation with Dialogue Memory
  • No Ads, Ever!
  • Access to Our Best AI Platform: Flex AI - Your personal assistant for all your inquiries!
Become a Member

Other questions asked by students

Basic Math
1.2K views

Given a normal distribution with mu equals 100 and sigma equals 10 comma complete parts​ (a)...

Biology
1.2K views

Cell Question Describe the structure and function of each of the following: lysosomes, peroxisomes, vacuoles, mitochondria, chloroplasts, plastids,...

General Management
1.2K views

LCOE for Wave Dragon 15 yrs, 5% interest  Cost + Installation = $10 million, O&M = 0.15M/year   Energy =...

Physics
1.2K views

What is the magnitude of the force between a charge of -7.5 x 10 C...

Geometry
1.2K views

3 Draw the image of the figure after a rotation of 180 around O OA...

Geometry
1.2K views

am How do we know that alleles actually separate during gamete formation A Scientists are...

Basic Math
1.2K views

How tall is a building that casts a 66 ft shadow when the angle of...

Algebra
1.2K views

Kelsey is 5 years older than her sister Misty The product of their ages in...

Accounting
1.2K views

1. The following selected financial data pertain to four unidentified companies:...

Accounting
1.2K views

Question: In 2015 a company bought new construction equipment for $100,000. The equipment was sold...

Accounting
1.2K views

Hello, Hope you are doing well. So we were given this MOCK assessment to help...

Accounting
1.2K views

TreeHold Corp. designs and builds custom harvesting equipment for logging companies across Canada. The company,...