I am attempting to factor an $N^{\text{th}}$ degree polynomial with coefficients strictly equal to $1$ given by the equation

$$\sum_{n=1}^{N} x^n$$

Although the Galois group for anything beyond a quartic is not generally soluble, I had hoped that an existing result had been established for this particular case. If not, I was curious if generalizing Tchirhausen transforms to the $N^{\text{th}}$ order and employing the Lagrange inversion theorem would allow me to examine series solutions with a special case being the Bring ultraradicals.