show that P=x^(9999) +x^(8888) +x^(7777) +x^(6666) +x^(5555) +x^(4444) +x^(3333) +x^(2222) +x^(1111) +1 Q=x^9 +x^8 +x^7 +x^6 +x^5 +x^4 +x^3 +x^2 +x+1 prove P is divisible by Q


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Question Number 58246 by tanmay last updated on 20/Apr/19

$s h o w t h a t$ $P = x^{9999} + x^{8888} + x^{7777} + x^{6666} + x^{5555} + x^{4444} + x^{3333} + x^{2222} + x^{1111} + 1$ $Q = x^{9} + x^{8} + x^{7} + x^{6} + x^{5} + x^{4} + x^{3} + x^{2} + x + 1$ $p r o v e P i s d i v i s i b l e b y Q$
	Answered by 2pac last updated on 25/Apr/19

	$p (x) = q (x^{1111})$ $l e t a b e e t h e r o o t s o f Q (x)$ $s o ===> a^{10} = 1 ===> a^{1110} = 1 === a^{1111} = a$ $s o p (a) = Q (a^{1111}) = Q (a) = 0$ $===> a r o o t s o f Q i s a l s o r o o t o f P s o$
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