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inkyvoyd

  • 2 years ago

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

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  1. inkyvoyd
    • 2 years ago
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    just a general thought question, also I am going to bed so you might want to disregard this one

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

  3. nincompoop
    • 2 years ago
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    want a book?

  4. inkyvoyd
    • 2 years ago
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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

  5. wio
    • 2 years ago
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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 \(\pm i\)

  6. inkyvoyd
    • 2 years ago
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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.

  7. inkyvoyd
    • 2 years ago
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    or Pis, cause of the repeated multiplication

  8. ParthKohli
    • 2 years ago
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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.

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