VIsor of x" -x for some n. 11. Let F be a finite field of p" elements containing the prime subfield Z,. Show that if a e F is a generator of the cyclic group (F*, ·) of nonzero elements of F, then deg(a, Z,) = n.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
icon
Related questions
Topic Video
Question
Section 33 number 11
ebraie-elosure of Zz, and let a, P e
Using the results of this section, show that Za(a) = Z>(B).
zeros of x' + x² + 1 and of x³ +x+1, respectively.
Show that every irredueible pelynomiat in Z,xis a divisor of x" – x for some n.
11. Let F be a finite field of p" elements containing the prime subfield Z,. Show that if a e F is a generator of
the cyclic group (F*, ·) of nonzero elements of F, then deg(a, Z,) = n.
Transcribed Image Text:ebraie-elosure of Zz, and let a, P e Using the results of this section, show that Za(a) = Z>(B). zeros of x' + x² + 1 and of x³ +x+1, respectively. Show that every irredueible pelynomiat in Z,xis a divisor of x" – x for some n. 11. Let F be a finite field of p" elements containing the prime subfield Z,. Show that if a e F is a generator of the cyclic group (F*, ·) of nonzero elements of F, then deg(a, Z,) = n.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Knowledge Booster
Discrete Probability Distributions
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,