4 ms·
I think it's something like p(x) = smallest positive solution of z^5 + z - x. Compare sqrt(x) = smallest positive solution of z^2 - x. But it's a _long_ time s
by moomin 9y ago
I think it's something like p(x) = smallest positive solution of z^5 + z - x. Compare sqrt(x) = smallest positive solution of z^2 - x.
But it's a _long_ time since I've done Galois theory and I can't find a decent math exchange answer for it right now, so don't treat this as gospel.
- akalin 9y agoYeah, I think you're thinking of a Bring radical: https://en.wikipedia.org/wiki/Bring_radical https://en.wikipedia.org/wiki/Bring_radical Edit: Oh, but that only lets you solve some quintics. https://news.ycombinator.com/item?id=14686886 https://news.ycombinator.com/item?id=14686886 describes the functions you need to solve all quintics.