let take n a odd integer greater than 3
if I have to solve this system of $(n-3)/2$ linear equations with $(n-3)/2$ unknowns to find some propriety about the number n,
here is formula for every equations in the system: $(m^{2m-1}+m^0)x_1 + ... + (m^{2m-i}+m^{i-1})x_i + ... + (m^{2m-(n-3)/2}+m^{((n-3)/2)-1})x_{(n-3)/2}=\frac{(m+1)^n-m^n-nm^{n-1}-nm-1}{m^2}$
(the first equation is when m=1,the second when m=2 and so on until m=$\frac{n-3}{2}$)
the system will look something like this for a given n:
\begin{cases} x_1 + x_2 + ... + x_{(n-3)/2} = 2^{n-1}-n-1\\ .\\.\\.\\(m^{2m-1}+m^0)x_1 + (m^{2m-2}+m^1)x_2 + ... + (m^{2m-i}+m^{i-1})x_i + ... + (m^{2m-(n-3)/2}+m^{((n-3)/2)-1})x_{(n-3)/2}=\frac{(m+1)^n-m^n-nm^{n-1}-nm-1}{m^2}\\.\\.\\.\\(\frac{n-3}{2}^{(2\frac{n-3}{2}-1)}+\frac{n-3}{2}^0)x_1 + (\frac{n-3}{2}^{(2\frac{n-3}{2}-2)}+\frac{n-3}{2}^1)x_2 + ... + (\frac{n-3}{2}^{(2\frac{n-3}{2}-i)}+\frac{n-3}{2}^{(i-1)})x_i + ... + (\frac{n-3}{2}^{(2\frac{n-3}{2}-\frac{n-3}{2})}+\frac{n-3}{2}^{(\frac{n-3}{2}-1)})x_{(n-3)/2}=\frac{(\frac{n-3}{2}+1)^n-\frac{n-3}{2}^n-n\frac{n-3}{2}^{n-1}-n\frac{n-3}{2}-1}{\frac{n-3}{2}^2}\end{cases}
Here is my main question:
What is the time complexity of this algorithm and what way can be use to find it?
Thank you very mutch.