if 11^(800) divide by 9 what will be the remainder?


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Question Number 203911 by Davidtim last updated on 01/Feb/24

$i f 11^{800} d i v i d e b y 9 w h a t w i l l b e t h e$ $r e m a i n d e r ?$
	Answered by deleteduser1 last updated on 01/Feb/24

	$11^{800} \equiv 2^{800} = {(2^{6})}^{133} {(2)}^{2} \equiv 4 (m o d 9)$
	Answered by Rasheed.Sindhi last updated on 02/Feb/24

	$I n s o m e d e t a i l :$ $11^{800} \equiv 2^{800} \equiv x (m o d 9) (s a y)$ $∵ \gcd (2, 9) = 1$ $∴ 2^{ϕ (9)} \equiv 1 (m o d 9)$ $2^{6} \equiv 1 (m o d 9)$ ${(2^{6})}^{133} \equiv 1^{133} (m o d 9)$ $2^{798} \equiv 1 (m o d 9)$ $2^{798} . 2^{2} \equiv 1 . 2^{2} (m o d 9)$ $2^{800} \equiv 4 (m o d 9)$ $x \equiv 4 (m o d 9)$
	Commented by Davidtim last updated on 05/Feb/24

	$I {d i d n}^{'} t g e t f u l l r e s u l t, w o u l d y o u m i n d s o l v e d e s r i b e l y ?$
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