For which odd positive integer $n$ , is it true that $-1$ is not a positive power of $2$ modulo $n$ i.e. $[-1] \ne [2^k] , \forall k >0$ in $\mathbb Z_n$ ? Is there any ( at least sufficient ) characterization for such odd $n$ ?
( I have only found $n=7$ is such a number ) . Please help . Thanks in advance