20^(11) −1 = ...(mod 1000)


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Question Number 198400 by cortano12 last updated on 19/Oct/23

$20^{11} - 1 = . . . (\mod 1000)$
	Answered by MM42 last updated on 19/Oct/23

	$20^{11} - 1 \overset{1000}{\equiv} - 1 \overset{1000}{\equiv} 999$
	Answered by mr W last updated on 19/Oct/23

	$20^{11} = 2^{11} \times 10^{11} = 204800000000000$ $20^{11} - 1 = 204799999999999$ $. . .$
	Answered by BaliramKumar last updated on 19/Oct/23

	$\frac{20^{11} - 1}{1000} = \frac{20^{2} {(20^{3})}^{3} - 1}{1000} = \frac{20^{2} {(8000)}^{3} - 1}{1000}$ $\Rightarrow \frac{- 1}{1000} = - 1 + 1000 = 999$
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