Abstract Algebra: Theory and Applications · Problem 17.5.24

Integral Domains — Thomas Judson

Mathematics — Abstract Algebra · polynomial-zeros

Problem

Show that xp−xx^p - x has pp distinct zeros in Zp\mathbb{Z}_p, for any prime pp. Conclude that xp−x=x(x−1)(x−2)⋯(x−(p−1)).x^p - x = x(x-1)(x-2)\cdots(x-(p-1)).

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