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Can you find an element $x$ in a field of characteristic $p$, ($p$ prime number), such that it is not equal to its inverse? And how this depends on the cardinality of the field?

Thanks.

Xam
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Hua Ying
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1 Answers1

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If $p=2$, there is one and only on such element, which is $1$.

Otherwise, there are two such elements, which are $1$ and $-1$.

This is so because $x=x^{-1}\iff x^2=1$.

José Carlos Santos
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