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\begin{array}{c}{\text { Show that } x^{p}-x \text { has } p \text { distinct zeros in } \mathbb{Z}_{p}, \text { for any prime } p .

 Show that xpx has p distinct zeros in Zp, for any prime p. Conclude that xpx=x(x1)(x2)(x(p1))

begin{array}{c}{text { Show that } x^{p}-x text { has } p text { distinct zeros in } mathbb{Z}_{p}, text { for any prime } p . text { Conclude that }} \ {x^{p}-x=x(x-1)(x-2) cdots(x-(p-1))}end{array}

Top Answer

By using of Fermat's Little Theorem, that... View the full answer

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