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Let p be a prime. Show that xpn −x+1 ∈ Fp[x] is irreducible iff either (1) p = 2 and n =1,2 or (2) p ≥3 and n=1

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter3: Groups

Section3.2: Properties Of Group Elements

Problem 30E: 30. Prove statement of Theorem : for all integers .

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Let p be a prime. Show that xpn −x+1 ∈ Fp[x] is irreducible iff either (1) p = 2 and n =1,2 or (2) p ≥3 and n=1.

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