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Question Number 208980 by lmcp1203 last updated on 30/Jun/24

$$please.find{2}^{{11001}^{666}}mod23thanks.$$

Answered by A5T last updated on 30/Jun/24

$$2^{{11001}^{666}}mod\left(23\right)\equiv 2^{{11001}^{666}\left[mod\varphi \left(23\right)\right]}\equiv 2\left(mod23\right)$$$$\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}$$$$\varphi \left(23\right)=22;{11001}^{666}\left(mod22\right)\equiv 1^{666}=1\left(mod22\right)$$

Commented by lmcp1203 last updated on 30/Jun/24

$$thanks$$

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