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Question Number 212033 by RojaTaniya last updated on 27/Sep/24

$$Findlasttwodigitof\mid {33}^{22}-{22}^{33}\mid$$

Answered by Frix last updated on 27/Sep/24

$${22}^{33}-{33}^{22}=$$$$199502557353381471378605391983038967797408063$$

Commented by MATHEMATICSAM last updated on 27/Sep/24

$$\mathrm{Bruh}$$

Answered by A5T last updated on 27/Sep/24

$${22}^{33}=2^{33}\times {11}^{33}={11}^{22}\left({11}^{11}\right){\left(8\right)}^{11}>{11}^{22}\times 3^{22}={33}^{22}$$$$\Rightarrow \mid {33}^{22}-{22}^{33}\mid ={22}^{33}-{33}^{22}\equiv 3\left(mod4\right);$$$${22}^{33}-{33}^{22}\equiv 2-64\equiv 13\left(mod25\right)$$$$\Rightarrow {22}^{33}-{33}^{22}\equiv 63\left(mod100\right)$$

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