Решете m^frac{1{2^k}}=1

$$m ^ { \frac { 1 } { 2 ^ { k } } } = 1$$

Реши за k (complex solution)

$$\left\{\begin{matrix}k\in \cup n_{2},\frac{-\ln(\frac{2n_{1}i}{\ln(m)})-\ln(\pi )}{\ln(2)}-\frac{2\pi n_{2}i}{\ln(2)}\text{, }n_{1}\in \mathrm{Z}\text{, }n_{1}\neq 0\text{, }&m\neq 1\text{ and }m\neq 0\\k\in \mathrm{C}\text{, }&m=1\end{matrix}\right,$$

Реши за m (complex solution)

$$m=\frac{1}{e^{2\pi n_{1}\left(Im(\frac{1}{2^{k}})+iRe(\frac{1}{2^{k}})\right)\left(\left(Re(2^{k})\right)^{2}+\left(Im(2^{k})\right)^{2}\right)}}$$

$$n_{1}\in \mathrm{Z}$$

Реши за k

$$k\in \mathrm{R}$$

$$m=1$$

Реши за m

$$\left\{\begin{matrix}\\m=1\text{, }&\text{unconditionally}\\m=-1\text{, }&Numerator(\frac{1}{2^{k}})\text{bmod}2=0\text{ and }Denominator(\frac{1}{2^{k}})\text{bmod}2=1\end{matrix}\right,$$