If g(x) is irreducible over GF( p) and g(x) divides x pn - x, prove thatdeg g(x) divides n.

Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter9: Polynomial And Rational Functions
Section9.2: Remainder And Factor Theorems
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If g(x) is irreducible over GF( p) and g(x) divides x pn - x, prove that
deg g(x) divides n.

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