Question: For n Z+, n > 2, let f(x) Zn[x]. Prove that if a, b Z and a = b (mod n), then

For n ∈ Z+, n > 2, let f(x) ∈ Zn[x]. Prove that if a, b ∈ Z and a = b (mod n), then f(a) = f(b) (mod n).

Step by Step Solution

★★★★★

3.45 Rating (165 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

If a b mod n then by mathematical induction it follows that ... View full answer

blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Document Format (1 attachment)

Word file Icon

954-M-L-A-L-S (8613).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

Q:

Prove that if a > 1/2, then is differentiable at (0, 0). ylog(2 y x y) (x, y) (0, 0) (0.0) f(a. y)

Q:

Let S R be nonempty. Prove that if a number u in R has the properties: (i) for every n N the number u - 1/n is not an upper bound of S, and (ii) for every number n N the number u + 1/n is an upper...

Q:

Let f, g be real functions j and for each x Dom (f) Dom (g) define (f g)(x) :=max{f(x),g(x)} and (f g)(x) := mm{f (x), g(x)}. a) Prove that and for all x Dom (f) Dom (g). b) Prove that if...

Q:

Section 4.1: (page 247) Numbers 1, 3, 7-13 odd, 19-23 odd Section 4.2: (page 260) Numbers 1, 5, 13, 19a, 20a Section 4.3: (page 270) Numbers 1-5 odd textbroker.com X Final Exam X X Canvas LMS X...

Q:

1. (30 pts) Let A = {4, 5, 6} and B = {5,6, 7} and define relations R, S, and T from A to B as follows: For all (x,y)e AXB, (x,y)e R means that x 2y , x_yeZ, 2 T = {(4,7),(555),(6,7)}. 3) Draw arrow...

Q:

1. We learned that when a force Fi is applied to triangle A, the x-component of the force that ends up actually being applied to the pin P is f ( , ) = F sin ( ) sin ( ) cos ( ) . Assuming F is...

Q:

1. In Topic 4.2 (The Definite Integral II), we considered f(x)=19-x on [-3, 3] We know that the function produces a semi-circle and the definite integral gives the area between the curve and the...

Q:

Let A, B be sets. Define: (a) the Cartesian product (A B) (b) the set of relations R between A and B (c) the identity relation A on the set A [3 marks] Suppose S, T are relations between A and B, and...

Q:

Department of Computer Science & Software Engineering Comp232 Mathematics for Computer Science Winter 2017 Assignment 3. Due date: March 30, by 23:59 EDT 1. For each of the following, determine...

Q:

For monotone functions f, f0: P Q between posets (P, vP ) and (Q, vQ), let f v f(i) Prove that the binary relation v is a partial order. [3 marks] (ii) For monotone functions between posets p : P 0...

Q:

5 How important is exclusivity on a licence deal? 6 Examine the intellectual property concerns for potential food brand owner customers regarding whether their competitors may get access to the...

Q:

At December 31, 2010, Ambuir Corporation had a future tax liability of $35,000. At December 31, 2011, the future tax liability is $52,000. The corporation's 2011 current tax expense is $53,000. What...

Q:

Is your company pursuing any of the qualityenhancing practices discussed in this chapter?

Q:

You are the project manager of the GHK Project. You and the manufacturer have agreed to substitute the type of plastic used in the product to a slightly thicker grade should there be more than a...

Q:

Two varieties of flu spread through a school one winter. The probability that a student gets both varieties is .18. The probability that a student gets neither variety is .42. Having one variety of...

Q:

This table gives counts of different types of paperclips in Maricela's paperclip holder. a. Create a Venn diagram of the probabilities of picking each kind of clip if one is selected at random. Use...

Q:

Which of these numbers comes from a geometric random variable? Explain. a. The number of phone calls a telemarketer makes until she makes a sale b. The number of cats in the home of a cat owner c....

Q:

Question 15 1.5 pts Today you observe the folowing quotes: Spot GBPUSD - $1.06 60 Day Forward GBPUSD - $1.26 In 60 day you expect to receive 171,078 British Pounds. In 60 days you expect the GBPUSD...

Q:

Assume our bank issued a $50 million, one-year-maturity CD, denominated in British pounds. Later that day, the bank invested $25 million in a US Treasury Bill and $25 million in a pound-denominated...

Q:

Which one of the following statements is false? A) Numerical measures can help investors decide if it is time to buy or sell a stock. B) Future earnings may be one of the most significant factors to...