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Extreme Polynomial Division problem

Algebra Level 5

Find the remainder when $x^{1001}-1$ is divided by $x^4+x^3+2x^2+x+1$ .

-1+x

x^4-x^3

x^2-x

-x^4+x^3

-x^2+x

x+1

x^3-x^2

-x^3+x^2

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by Michael Wang

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