What is the remainder when 17^(200) is divided by 18


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Question Number 34139 by NECx last updated on 01/May/18

$W h a t i s t h e r e m a i n d e r w h e n$ $17^{200} i s d i v i d e d b y 18$
	Answered by tanmay.chaudhury50@gmail.com last updated on 01/May/18

	$l e t n = 200$ $s o p r o b l e m i s {(18 - 1)}^{n}$ $18^{n} - 18_{C_{1}} . 18^{n - 1} + 18_{C_{2}} . 18^{n - 2} . . . . {(- 1)}^{n}$ $s o r e m a i n d e r i s {(- 1)}^{n} h e r e n = 200 s o$ $r e m a i n d e r i s 1$
	Answered by Rasheed.Sindhi last updated on 04/May/18

	$17 \equiv - 1 (\mod 18)$ ${(17)}^{200} \equiv {(- 1)}^{200} = 1 (\mod 18)$ ${(17)}^{200} \equiv 1 (\mod 18)$
	Commented by Rasheed.Sindhi last updated on 09/May/18

	$Mr NECx pl confirm the answer .$
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