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Is there a quick analytic way to solve this polynomial?

  1. May 23, 2013 #1
    ny = x^(n-1) + x^(n-2) + ... + x + 1

    for a certain y and n (>10000) with y!=1 and ny > 1.

    Is there an analytic way to solve this? Thank you.
     
  2. jcsd
  3. May 23, 2013 #2
    yes, you can interpret it as a sum. that way you can work with it easily.
    from that point on you can prove any type of given question whatsoever
     

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  4. May 23, 2013 #3
    thank you for your reply, my question was though how to find x for let's say y = 4 and n = 10000 in the shortest possible amount of time. i know that's not feasible for polynomials of this size in general, but i don't know if there are any special kinds and solution strategies, since this one looks quite simple.
    i should have added that i am only interested in real solutions which only exist for n*y >= 1.
     
  5. May 23, 2013 #4

    SteamKing

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    I think poster #2 is confused. The OP was looking to solve the polynomial, not take derivatives or integrals.

    AFAIK, there is no simple analytic way to solve polynomials with degree 5 and greater.
     
  6. May 23, 2013 #5

    mathman

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    The sum on the right = (1-xn)/(1-x).

    Can you go from there?
     
  7. May 23, 2013 #6
    incredible. thanks a lot!
     
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