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Given a polynomial constraint equation in $n$ variables, can one conclude that the sum of the variables is non-negative?
Currently I'm stuck as follows;
at least a positive proof if $n=3$ would be a great nice-to-have!
Consider real numbers $x_1,x_2,\dots,x_n$ satisfying
$$\prod^n_{k=1}\left(1-x_k^2\right)\:=\:\...
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