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Nimber $2^{2^k} - 1$ is a multiplicative generator of $[2^{2^k}]$?
Let $t = 2^{2^k}$, and consider the field $[t]$ of nimbers below $t$. For $k \leq 6$ one can check that $t - 1$ (in the usual arithmetic sense) is a multiplicative generator of $[t] \backslash \{0\}$. ...
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