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Let $\xi\in GR(4^{m})$ and $\xi$ is of order $2^{m}-1$. If $\pm\xi^{j}\pm\xi^{k}$ is not invertible for $0\leq j, where $m\geq 2$, then why $\pm\xi^{j}\pm\xi^{k}=2\lambda$, where $\lambda\in GR(4^{m})$?

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