x'- Excrcése l Let k be a field. Prove that the set of irreducible pelynomials over k is infinite. Exercise 2. (a)Prove that a"1 = ñ (x-3') in %3D where 3- (6) Let F be a finite field and IF(=. Prove that ax% _c 7 (x-a) in F[x]. %3D KEF
x'- Excrcése l Let k be a field. Prove that the set of irreducible pelynomials over k is infinite. Exercise 2. (a)Prove that a"1 = ñ (x-3') in %3D where 3- (6) Let F be a finite field and IF(=. Prove that ax% _c 7 (x-a) in F[x]. %3D KEF
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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hi, please help me with exercise 2
![Excreése I Let k be a ficld. Prove that the sel
of irreducible pelynomicls
Exercise 2. (a)Prove that x-1 = 1 (x-34) in
C [xJ, where 3 = e
(6) fat F be a finite field and (Fl=q . Prove
that x%_x
over k is infinite.
トー1
7 (x-a)
dE F
in F[x].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fab4ef834-bbcc-4669-a4c3-4f579799562b%2Fcd857009-49c4-4dba-8a78-af28406e670e%2Fzon6us_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Excreése I Let k be a ficld. Prove that the sel
of irreducible pelynomicls
Exercise 2. (a)Prove that x-1 = 1 (x-34) in
C [xJ, where 3 = e
(6) fat F be a finite field and (Fl=q . Prove
that x%_x
over k is infinite.
トー1
7 (x-a)
dE F
in F[x].
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