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Question Number 198418 by cortano12 last updated on 19/Oct/23

$${20}^{22}-1=...\left(\mathrm{mod}1000\right)$$$$$$

Answered by BaliramKumar last updated on 19/Oct/23

$$$$$$\frac{{20}^{22}-1}{1000}=\frac{20{\left({20}^3\right)}^7-1}{1000}=\frac{20{\left(8000\right)}^7-1}{1000}$$$$\frac{20{\left(8\cancel{000}\right)}^7}{1\cancel{000}}-\frac{1}{1000}=(0-1)\mathrm{remainder}$$$$\Rightarrow -1+1000=999$$

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