Find the irreducible tactors of 2++² + 2x +1 in Zs[z] For which of the primes p E {3,5} can we construct a field of order p² by using the polynomial + 1? If its possible to construct a field write down all its elements and compute (1+2r}(2+2r) within the field. What is the relation between the two elements (1 + 2x) and (2 +2r)?
Find the irreducible tactors of 2++² + 2x +1 in Zs[z] For which of the primes p E {3,5} can we construct a field of order p² by using the polynomial + 1? If its possible to construct a field write down all its elements and compute (1+2r}(2+2r) within the field. What is the relation between the two elements (1 + 2x) and (2 +2r)?
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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![Problem 5
a) Find the irreducible tactors of
++² + 2r+1 in Z3[x]
b) For which of the primes p€ {3,5} can we construct a field of order p² by using the polynomial z?+1?
If its possible to construct a field write down all its elements and compute (1+21)(2+2r) within the
field. What is the relation between the two elements (1+ 2x) and (2 +2.r)?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F10b8abaa-0bdc-46e8-8a29-eb532c69e836%2F05fb53e3-5eaa-452c-996b-f651e09a0e8f%2F6ssju2m_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Problem 5
a) Find the irreducible tactors of
++² + 2r+1 in Z3[x]
b) For which of the primes p€ {3,5} can we construct a field of order p² by using the polynomial z?+1?
If its possible to construct a field write down all its elements and compute (1+21)(2+2r) within the
field. What is the relation between the two elements (1+ 2x) and (2 +2.r)?
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