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inkyvoyd Group Title

What is the general formula to factoring x^n+1 where n is a natural number?

  • one year ago
  • one year ago

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  1. inkyvoyd Group Title
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    just a general thought question, also I am going to bed so you might want to disregard this one

    • one year ago
  2. inkyvoyd Group Title
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    but bonus points if you can use full mathematical symbols!!! it'd be such a great learning experience for me :)

    • one year ago
  3. nincompoop Group Title
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    want a book?

    • one year ago
  4. inkyvoyd Group Title
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    also, some sort of hint for the dedicated, you could probably reformulate this problem in terms of the nth roots of unity

    • one year ago
  5. wio Group Title
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    It's easier to think of it as \[ x^n = -1 \]So we have two cases. Either \(n\) is odd, and the roots are just \(-1\) or \(n\) is even, and the roots are \(\pm i\)

    • one year ago
  6. inkyvoyd Group Title
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    @wio , so starting with that I could probably write the solution in terms of 2 sigmas (one for n is odd and one for n is even)? I think I"l try to do this one tomorrow actually. GOod practice for someone like me. THanks guys.

    • one year ago
  7. inkyvoyd Group Title
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    or Pis, cause of the repeated multiplication

    • one year ago
  8. ParthKohli Group Title
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    Depends on how you want to factor it. It does have roots that are complex, but it doesn't have real roots, so you can't factorize it.

    • one year ago
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