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Let p be a prime that does not divide n. Prove that Φpn(x) =Φn(x p)/Φn(x).

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter8: Polynomials

Section8.3: Factorization In F [x]

Problem 23E: Let f(x),g(x),h(x)F[x] where f(x) and g(x) are relatively prime. If h(x)f(x), prove that h(x) and...

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Let p be a prime that does not divide n. Prove that Φ_pn(x) =Φ_n(x ^p)/Φ_n(x).

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