The remainder of 13^(13) when divided by 99 is


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Question Number 169159 by SLVR last updated on 25/Apr/22

$T h e r e m a i n d e r o f$ $13^{13} w h e n$ $d i v i d e d b y 99 i s$
Commented by SLVR last updated on 25/Apr/22

$k i n d l y s o l v e . .$
	Answered by Rasheed.Sindhi last updated on 25/Apr/22

	$13^{2} \equiv 169 (m o d 99)$ $13^{2} \equiv 169 - 99 = 70 (m o d 99)$ $13^{2} \times 13 \equiv 70 \times 13 (m o d 99)$ $13^{3} \equiv 910 (m o d 99)$ $13^{3} \equiv 910 - 99 \times 9 = 19 (m o d 99)$ ${(13^{3})}^{2} \equiv 19^{2} = 361 (m o d 99)$ $13^{6} \equiv 361 - 99 \times 3 = 64 (m o d 99)$ ${(13^{6})}^{2} \equiv 64^{2} = 4096 (m o d 99)$ $13^{12} \equiv 4096 - 99 \times 41 = 37 (m o d 99)$ $13^{12} \cdot 13 \equiv 37 \times 13 = 481 (m o d 99)$ $13^{13} \equiv 481 - 99 \times 4 = 85 (m o d 99)$ $1 y 3^{13} \equiv 85 (m o d 99)$
	Commented by SLVR last updated on 25/Apr/22

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