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How can I use partial-fraction decomposition for this fraction?

$f(x)=\dfrac{1}{1+x^{7}}$

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closed as off-topic by C. Falcon, Namaste, TastyRomeo, zhoraster, pjs36 Jan 15 '17 at 17:43

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The roots of $x^7+1$ are $\{-1, -\zeta, -\zeta^2,-\zeta^3,-\zeta^4,-\zeta^5,-\zeta^6 \}$ where $\zeta = \cos(2\pi/7)+i\sin(2\pi/7)$.

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  • $\begingroup$ how you arrive in this solution? Can you give me your method? Thanks $\endgroup$ – k2532184 Jan 15 '17 at 16:53
  • $\begingroup$ These are the classic roots of unity as expressed as roots of the cyclotomic polynomials. $\endgroup$ – Marc Bogaerts Jan 15 '17 at 17:02
  • $\begingroup$ This is an easier reference. $\endgroup$ – Marc Bogaerts Jan 15 '17 at 17:08
  • $\begingroup$ I don't know what you are saying to me. Can you do in a sheet of paper and send to me, how you get all the roots? $\endgroup$ – k2532184 Jan 15 '17 at 17:10
  • $\begingroup$ Did you click on the links? $\endgroup$ – Marc Bogaerts Jan 15 '17 at 17:12

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