Logo
Home Study Material Contact Search
AI Chat FREE
  1. mathematics
  2. advance math
  3. 24. show that (x ^p) ? x has p distinct zeros in z

24. Show that (x ^p) ? x has p distinct zeros in Zp, for any prime...

60.2K

Verified Solution

Question

Advance Math

24. Show that (x ^p) ? x has p distinct zeros in Zp, for anyprime p. Conclude that (x ^p) ? x = x(x ? 1)(x ? 2)· · ·(x ? (p ?1)).

(this is not as simple as showing that each element inZp is a root -- after all, we've

seen that in Z6[x], the polynomialx^2-5x has 4 roots, 0, 5, 2, and 3, but x^2-5 is not equal to(x-0)(x-5)(x-2)(x-3))

Answer & Explanation Solved by verified expert
4.0 Ratings (642 Votes)
Recall Fermats little theorem states that if p is a primenumber then for any integer a Then choose any element then we can find a unique integer be such that the image of a in is Thengives us the fact in the ring rather field Thusthis proves the fact that every element of is    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: Zin AI - Your personal assistant for all your inquiries!
Become a Member

Other questions asked by students

Q

Solve the linear programming problem by the method of corners. Find the minimum and maximum of P...

Advance Math
Q

Gozilla (western lowland Gorilla) 1. Social Organization (How is this species socially organized? Use term like nuclear...

Biology
Q

patient enters your respiratory laboratory complaining of feeling lightheaded. You measure their tidal volume at 100ml...

Medical Sciences
Q

300 word minimum. ---------------------------------------------------- Head to the Internet and find an example of a company's organizational chart. Analyze the...

General Management
Q

Example Vinegar has a pH of 3 If you add sodium hydroxide NaOH what will...

Biology
Q

Find the distance d (P1, P2) between the points P? and P2P?=(1,-2), P?=(2,6)(P?, P?) =(Simplify...

Basic Math
Q

The combination of cold temperatures and wind speed determine what is called wind chill. The...

Basic Math
Q

Assume the following demand curve: Q = 100,800 3,535(P). Calculate elasticity for a price...

Accounting
Q

2) Cozelle, Inc., purchased inventory costing $125,000 and sold 80% of the goods for $200,000...

Accounting
Q

Chapter 1 Homework Saved Help Save & Exit Submit Check my work 4 Part 1...

Accounting
Q

1) Name the four primary Farm Financial Statements

Accounting
Q

\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|} \hline \multicolumn{11}{|c|}{ Perpetual LIEO: } \\ \hline \multirow[b]{2}{*}{ Date } & \multicolumn{2}{|c|}{ Goods Purchased...

Accounting