Originally Posted by

**CaptainBlack** In the spirit of the challenge of finding the oldest unanswered post, this question is after a bit of jiggery pokery asking for solutions of:

$\displaystyle r^n-\frac{S}{t}r+\frac{S-t}{t}=0$

or rewritting this:

Can we find one or more real roots of:

$\displaystyle r^n-ar+b=0$

in closed form when $\displaystyle n>4$.

(The condition on $\displaystyle n$ is because we have the formulas for the roots for $\displaystyle n=1,\ 2,\ 3,\ 4$. Though something more elegant for the last two cases would be nice).

CB