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Question Number 189700 by DAVONG last updated on 20/Mar/23

Commented by Rasheed.Sindhi last updated on 21/Mar/23

$$a=21$$

Commented by mehdee42 last updated on 21/Mar/23

$${it}^{,}swrong.because$$$${21}^5\stackrel{100}{\equiv }01\Rightarrow {21}^{2020}\stackrel{100}{\equiv }01\Rightarrow {21}^{2022}\stackrel{100}{\equiv }{21}^2\stackrel{100}{\equiv }41$$

Answered by mehdee42 last updated on 21/Mar/23

$${11}^2\stackrel{100}{\equiv }21\Rightarrow {11}^{10}\stackrel{100}{\equiv }{21}^5\stackrel{100}{\equiv }01$$$$\Rightarrow {11}^{2020}\stackrel{100}{\equiv }01\Rightarrow {11}^{2022}\stackrel{100}{\equiv }21\Rightarrow a=11$$

Commented by Rasheed.Sindhi last updated on 22/Mar/23

$${It}^{\prime }s{a}^{2021},not{a}^{2022}$$

Commented by Rasheed.Sindhi last updated on 22/Mar/23

$${21}^5\equiv 1\left(mod100\right)$$$${21}^{2020}\equiv 1\left(mod100\right)$$$${21}^{2020}\times 21\equiv 21\left(mod100\right)$$$${21}^{2021}\equiv 21\left(mod100\right)$$

Answered by talminator2856792 last updated on 22/Mar/23

$$...\mathrm{X}\mathrm{Y}1\times 11=...\mathrm{X}\mathrm{Y}10$$$$+...\mathrm{Y}1$$$$\overline{}\overline{}\overline{}\overline{}\overline{\mathrm{Y}}+1\overline{}\overline{1}$$$$$$$$\Rightarrow {11}^{...\mathrm{xyz}1}=...\mathrm{z}1$$$$$$$${11}^{2021}=...21$$$$a=11$$$$$$

Commented by Rasheed.Sindhi last updated on 22/Mar/23

$${11}^{2021}\ne ...21$$$${11}^{2021}=...11:$$$${11}^{10}\equiv 1\left(mod100\right)$$$${\left({11}^{10}\right)}^{202}\equiv 1^{202}\left(mod100\right)$$$$({11}^{2020}\times 11\equiv 1\times 11\left(mod100\right)$$$${11}^{2021}\equiv 11\left(mod11\right)$$$$$$

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