4. Write every non-zero element in F as powers of [x+1]. 5. Find the inverse of [x² + x + 1] in F. 6. Find the sum of [x + 1]³+ [x+1]5 + [x + 1]².
4. Write every non-zero element in F as powers of [x+1]. 5. Find the inverse of [x² + x + 1] in F. 6. Find the sum of [x + 1]³+ [x+1]5 + [x + 1]².
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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finite field part 4 5 6
![1. Show that F = Z₂[x] /< x²³ + x + 1 > is a field and find its order.
2. List the elements of F.
3. Show that F* is cyclic group generated by [x+1].
4. Write every non-zero element in F as powers of [x+1].
5. Find the inverse of [x² + x + 1] in F.
6. Find the sum of [x + 1]³ + [x + 1]5 + [x + 1]².
7. List the subfields of F.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc9a0e59f-21d0-430c-a3cc-cb29b1509c86%2F9fe68fa2-be95-4c28-94f6-69e411e4591f%2Fil2l28c_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. Show that F = Z₂[x] /< x²³ + x + 1 > is a field and find its order.
2. List the elements of F.
3. Show that F* is cyclic group generated by [x+1].
4. Write every non-zero element in F as powers of [x+1].
5. Find the inverse of [x² + x + 1] in F.
6. Find the sum of [x + 1]³ + [x + 1]5 + [x + 1]².
7. List the subfields of F.
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