Question

(2) Letn∈Z+ withn>1. Provethatif[a]n isaunitinZn,thenforeach[b]n ∈Zn,theequation[a]n⊙x=[b]n has a unique solution x ∈ Zn. Note: You must...

(2) Letn∈Z+ withn>1. Provethatif[a]n isaunitinZn,thenforeach[b]n ∈Zn,theequation[a]n⊙x=[b]n has a unique solution x ∈ Zn.
Note: You must find a solution to the equation and show that this solution is unique.
(3) Let n ∈ Z+ with n > 1, and let [a]n, [b]n ∈ Zn with [a]n ̸= [0]n. Prove that, if the equation [a]n ⊙ x = [b]n has no solution x ∈ Zn, then [a]n must be a zero divisor.
Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Prove that if x ∈ Zn − {0} and x has no common divisor with n...
Prove that if x ∈ Zn − {0} and x has no common divisor with n greater than 1, then x has a multiplicative inverse in (Zn − {0}, ·n). State the theorem about Euler’s φ function and show why this fact implies it.
Let Zn = {0, 1, 2, . . . , n − 1}, let · represent...
Let Zn = {0, 1, 2, . . . , n − 1}, let · represent multiplication (mod n), and let a ∈ Zn. Prove that there exists b ∈ Zn such that a · b = 1 if and only if gcd(a, n) = 1.
1. Let a ∈ Z and b ∈ N. Then there exist q ∈ Z and...
1. Let a ∈ Z and b ∈ N. Then there exist q ∈ Z and r ∈ Z with 0 ≤ r < b so that a = bq + r. 2. Let a ∈ Z and b ∈ N. If there exist q, q′ ∈ Z and r, r′ ∈ Z with 0 ≤ r, r′ < b so that a = bq + r = bq′ + r ′ , then q ′ = q and r...
Prove that for a square n ×n matrix A, Ax = b (1) has one and...
Prove that for a square n ×n matrix A, Ax = b (1) has one and only one solution if and only if A is invertible; i.e., that there exists a matrix n ×n matrix B such that AB = I = B A. NOTE 01: The statement or theorem is of the form P iff Q, where P is the statement “Equation (1) has a unique solution” and Q is the statement “The matrix A is invertible”. This means...
Let a, b, and n be integers with n > 1 and (a, n) = d....
Let a, b, and n be integers with n > 1 and (a, n) = d. Then (i)First prove that the equation a·x=b has solutions in n if and only if d|b. (ii) Next, prove that each of u, u+n′, u+ 2n′, . . . , u+ (d−1)n′ is a solution. Here,u is any particular solution guaranteed by (i), and n′=n/d. (iii) Show that the solutions listed above are distinct. (iv) Let v be any solution. Prove that v=u+kn′ for...
Let x ∼ N(μ,σ) and z = x−μ/σ. Show that a. E{z} = 0 b. E{(z...
Let x ∼ N(μ,σ) and z = x−μ/σ. Show that a. E{z} = 0 b. E{(z − E{z})2} = 1.
You are given a differential equation x[n+2] + 5x[n+1] + 6x[n] = n with start values...
You are given a differential equation x[n+2] + 5x[n+1] + 6x[n] = n with start values x[0] = 0 and x[1] = 0 Find the solution to this equation.
1. ∀n ∈ Z, prove that if ∃a, b ∈ Z such that a 2 +...
1. ∀n ∈ Z, prove that if ∃a, b ∈ Z such that a 2 + b 2 = n, then n 6≡ 3 (mod 4).
Prove that n is prime iff every linear equation ax ≡ b mod n, with a...
Prove that n is prime iff every linear equation ax ≡ b mod n, with a ≠ 0 mod n, has a unique solution x mod n.
1. Let a, b ∈ Z. Define f : Z → Z by f(n) = an...
1. Let a, b ∈ Z. Define f : Z → Z by f(n) = an + b. Prove that f is one to one if and only if a does not equal 0.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT