What is reminder when 4^(29) divided by 17


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Question Number 114401 by bemath last updated on 19/Sep/20

$W h a t i s r e m i n d e r w h e n 4^{29}$ $d i v i d e d b y 17$
	Answered by bobhans last updated on 19/Sep/20

	$b e c a u s e 16 = 4^{2} \equiv - 1 (m o d 17)$ $w e h a v e 4^{4} \equiv {(4^{2})}^{2} \equiv {(- 1)}^{2} \equiv 1 (m o d 17)$ $s o w e o b t a i n 4^{29} \equiv {(4^{4})}^{7} . 4 \equiv 1.4 \equiv 4 (m o d 17)$ $h e n c e t h e r e m a i n d e r o f 4^{29} u p o n$ $d i v i s i o n b y 17 i s e q u a l t o 4 .$
	Commented by bemath last updated on 19/Sep/20

	$g a v e k u d o s ✓ ♠$
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