Lagrange's Theorem (Number Theory)/Examples/Non-Prime Index

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Example of Use of Lagrange's Theorem (Number Theory)

This does not hold for composite number $p$.

For $p = 8$, the polynomial $x^2 - 1$ has $4$ roots $\eqclass 1 8, \eqclass 3 8, \eqclass 5 8, \eqclass 7 8$ in $\Z_p$ and $4 > n = 2$.