# Is there a quick analytic way to solve this polynomial?

1. May 23, 2013

### DeanRichards

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. May 23, 2013

### ecpietscheck

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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3. May 23, 2013

### DeanRichards

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.

4. May 23, 2013

### SteamKing

Staff Emeritus
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.

5. May 23, 2013

### mathman

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

Can you go from there?

6. May 23, 2013

### DeanRichards

incredible. thanks a lot!