\[\begin{array}{l} {x^{{2^k}}} \equiv - 1\left( {\bmod p} \right) \Rightarrow {x^{{2^{k + 1}}}} \equiv 1\left( {\bmod p} \right) \hfill \\ {\operatorname{ord} _p}x = {2^{k + 1}} \Rightarrow {2^{k + 1}}|p - 1 \hfill \\ \end{array}\]