Newton's inequalities

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In mathematics, the Newton inequalities, named after Issac Newton, establishes that given real numbers

a1,a2,...,an,

and if

σk

denotes the k-th elementary symmetric function in a1,a2,...,an, then the elementary symmetric mean given by

S_k = \frac{\sigma_k}{\binom{n}{k}}

satisfies the inequality

S_{k-1}S_{k+1}\le S_k

with equality if and only if all the numbers ai are equal.

[edit] See also

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