Is there a quick analytic way to solve this polynomial?

[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.

 

[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

 

[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.

 

[SteamKing]

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.

 

[mathman]

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.

The sum on the right = (1-xⁿ)/(1-x).

Can you go from there?

 

[DeanRichards]

The sum on the right = (1-xⁿ)/(1-x).

Can you go from there?

incredible. thanks a lot!