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Is it divisible?

Algebra Level 3

$x^{9999}+x^{8888}+x^{7777}+ \cdots+x^{1111}+x^{0}$ is divisible by which of the following polynomials?

x^{8}+x^{6}+x^{4}+x^{2}

x^{9}+x^{7}+x^{5}+x^{3}+x

x+1

x-1

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by Piyush Kumar Behera

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