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Math Help - Polynomials and Prime Fields

  1. #1
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    Polynomials and Prime Fields

    Show that if f(x) = x^p - x belongs to Fp[x], then its polynomial function f^b: Fp --> Fp is identically zero.

    Note: Fp refers to a prime field.
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  2. #2
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    (\mathbb{F}_p^*,\times) is a (cyclic) group of order p-1.

    Therefore: \forall a\in \mathbb{F}_p, a^p=a, and the polynomial function f:\mathbb{F}_p\rightarrow\mathbb{F}_p:a\mapsto a^p-a is the zero function.
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