1. Let q-p" be a prime power. Show that X+ 1 is irreducible in F [X] if and only if q=3 mod4. (Hint: Use the fact that F is cyclic, also since its an if and only if please prove both directions)
1. Let q-p" be a prime power. Show that X+ 1 is irreducible in F [X] if and only if q=3 mod4. (Hint: Use the fact that F is cyclic, also since its an if and only if please prove both directions)
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 55RE
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![1. Let q-p" be a prime power. Show that X+ 1 is irreducible in F_[X] if
and only if q=3 mod4. (Hint: Use the fact that F
is cyclic, also since
its an if and only if please prove both directions)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F175e7cec-5184-4e8f-b438-5e0c4b948ad8%2F7ba358f3-3a07-4a62-9f4b-69cce362b1b0%2F70u3pj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. Let q-p" be a prime power. Show that X+ 1 is irreducible in F_[X] if
and only if q=3 mod4. (Hint: Use the fact that F
is cyclic, also since
its an if and only if please prove both directions)
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