[FOM] Need reference on result about polynomial equations
joeshipman@aol.com
joeshipman at aol.com
Sun Feb 15 21:33:33 EST 2009
Although the general quintic equation is not solvable by radicals, it
does have a general algebraic solution in terms of functions of one
variable (in particular, in terms of radicals of degrees 2,3, and 5
plus the "Bring Radical" solution of x^5+x=a,which is an analytic
function of a single variable).
I have read that this cannot be done for the sextic -- no combination
of analytic functions of one variable solves the general sixth degree
equation.
Can anyone give me a reference (in English, preferably online) for this
result? And how high does the degree have to get before there is no
general solution in terms of (analytic) functions of two variables?
-- JS
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