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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)

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)

Advanced Engineering Mathematics
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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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)
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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