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Find the remainder when the polynomial $x^{1000}$ is divided by the polynomial $(x^2 + 1)(x + 1).$

 
 Jan 7, 2021
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We can use long division.  We get a quotient of x^997 - x^996 + x^994 - x^993 + ... and a remainder of x^2 + x + 1.

 
 Jan 8, 2021

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