Question

In: Advanced Math

Suppose {a1,...,am} is a complete set of representatives for Z/mZ. Show: (i) If (b,m)=1, then{b*a1,...,b*am}is a...

Suppose {a1,...,am} is a complete set of representatives for Z/mZ. Show:

(i) If (b,m)=1, then{b*a1,...,b*am}is a complete set of
representatives.

(ii) If (b,m)> 1, then{b*a1,...,b*am}is not a
complete set of representatives.

Solutions

Expert Solution

Colby Messinger answered 1 year ago
Next > < Previous

Related Solutions

Prove (Z/mZ)/(nZ/mZ) is isomorphic to Z/nZ where n and m are integers greater than 1 and...
Prove (Z/mZ)/(nZ/mZ) is isomorphic to Z/nZ where n and m are integers greater than 1 and n divides m.
(3) Let m be a positive integer. (a) Prove that Z/mZ is a commutative ring. (b)...
(3) Let m be a positive integer. (a) Prove that Z/mZ is a commutative ring. (b) Prove that if m is composite, then Z/mZ is not a field. (4) Let m be an odd positive integer. Prove that every integer is congruent modulo m to exactly one element in the set of even integers {0, 2, 4, 6, , . . . , 2m− 2}
Consider the group Z/mZ ⊕ Z/nZ, for any positive integers m and n that are divisible...
Consider the group Z/mZ ⊕ Z/nZ, for any positive integers m and n that are divisible by 4. How many elements of order 4 does G have, and why?
I have to complete Form 1040, and Schedules 1, A, and B. I am fairly lost...
I have to complete Form 1040, and Schedules 1, A, and B. I am fairly lost at this moment, so anything can help Martin S. Albert (Social Security number 111-11-1111) is 39 years old and is married to Michele R. Albert (Social Security number 123-45-6789). The Alberts live at 512 Ferry Road, Newport News, VA 23601. They file a joint return and have two dependent children, Charlene, age 17, and Jordan, age 18. Charlene’s Social Security number is 123-45-6788, and...
show that if I is uncountable,then 2I is not metrizable. hint: Suppose I as index set.
show that if I is uncountable,then 2I is not metrizable. hint: Suppose I as index set.
Suppose A = {(a, b)| a, b ∈ Z} = Z × Z. Let R be...
Suppose A = {(a, b)| a, b ∈ Z} = Z × Z. Let R be the relation define on A where (a, b)R(c, d) means that 2 a + d = b + 2 c. a. Prove that R is an equivalence relation. b. Find the equivalence classes [(−1, 1)] and [(−4, −2)].
4. Show that the set A = {fm,b : R → R | m does not...
4. Show that the set A = {fm,b : R → R | m does not equal 0 and fm,b(x) = mx + b, m, b ∈ R} forms a group under composition of functions. (The set A is called the set of affine functions from R to R.)
I am so lost on this. I am making a B in this class but I...
I am so lost on this. I am making a B in this class but I can not seem to get this project completed. Please help. ACC-120 Project – Financial Accounting This assignment supports the following outcomes: ·          Prepare journal and ledger entries for a service or merchandising business. ·          Prepare year-end statements for a service or merchandising business. ·          Report cost decisions using accounting principles and financial statement analysis. ·          Evaluate how knowledge, skills, and attitudes learned in this...
For given list of members in a universal set U. Members A B 1 a1 b1...
For given list of members in a universal set U. Members A B 1 a1 b1 2 a2 b1 3 a3 b2 4 a1 b2 5 a1 b2 6 a2 b1 7 a3 b1 8 a1 b2 9 a1 b2 10 a3 b2 Write Probability distribution table for (a) P(A, B) (b) P(A) (c) P(B) (d) P(A|B=b1)
Consider the relation R defined on the set Z as follows: ∀m, n ∈ Z, (m,...
Consider the relation R defined on the set Z as follows: ∀m, n ∈ Z, (m, n) ∈ R if and only if m + n = 2k for some integer k. For example, (3, 11) is in R because 3 + 11 = 14 = 2(7). (a) Is the relation reflexive? Prove or disprove. (b) Is the relation symmetric? Prove or disprove. (c) Is the relation transitive? Prove or disprove. (d) Is it an equivalence relation? Explain.
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT