Timeline for Does this equation has a closed-form solution for $t$? ($(1-p)\sum_{i=0}^{n}t^i = p\sum_{i=0}^{n}(1-t)^i)$)

11 events

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Jun 15, 2020 at 7:27	history	edited	CommunityBot		Commonmark migration
Nov 17, 2014 at 19:06	answer	added	Robert Israel		timeline score: 2
Nov 17, 2014 at 17:26	comment	added	Chris Wuthrich		The Galois group of the equation for $p=3/5$ and $n=7$ is $S_7$, which is not soluble. So don't expect a solution by radicals for $n=7$.
Nov 17, 2014 at 16:50	answer	added	joro		timeline score: 2
Nov 17, 2014 at 15:36	comment	added	R B		@joro - I have a closed form for $t(3,p)$, would love to hear about $t(5,p)$ !
Nov 17, 2014 at 15:35	comment	added	joro		I think I found closed form for n in {3,5}.
Nov 17, 2014 at 15:33	history	edited	R B	CC BY-SA 3.0	added 258 characters in body
Nov 17, 2014 at 14:57	history	edited	R B	CC BY-SA 3.0	deleted 2 characters in body
Nov 17, 2014 at 14:50	comment	added	GH from MO		Probably not. Most irreducible polynomials of degree $n>4$ have a non-solvable Galois group. Of course it would help if you defined more precisely what you mean by "closed form". Solvability in radicals is equivalent to a solvable Galois group for the polynomial.
Nov 17, 2014 at 14:10	history	edited	R B	CC BY-SA 3.0	edited body
Nov 17, 2014 at 13:47	history	asked	R B	CC BY-SA 3.0