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Find the remainder when $x^{44} + x^{33} + x^{22} + x^{11} + 1$ is divided by $x^4 + x^3 + x^2 + x + 1.$

 Nov 13, 2019
 #1
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By long division, the remainder is x^3 + x.

 Nov 13, 2019
 #2
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Find the remainder when \(x^{44} + x^{33} + x^{22} + x^{11} + 1\) is divided by \(x^4 + x^3 + x^2 + x + 1\).


\(\left(x^{44} + x^{33} + x^{22} + x^{11} + 1\right) :\left( x^4 + x^3 + x^2 + x + 1 \right) \\\\ = x^{40} - x^{39} + x^{35} - x^{34} + x^{30} - x^{28} + x^{25} - x^{23} + x^{20} - x^{17} + x^{15} - x^{12} + x^{10} - x^6 + x^5 - x + 1\)

 

laugh

 Nov 14, 2019
edited by heureka  Nov 14, 2019
edited by heureka  Nov 14, 2019

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