Newton's inequalities
In mathematics, the Newton inequalities are named after Isaac Newton. Suppose a1, a2, ..., an are real numbers and let denote the kth elementary symmetric function in a1, a2, ..., an. Then the elementary symmetric means, given by
satisfy the inequality
If all the numbers ai are nonzero, then equality holds if and only if all the numbers ai are equal. S1 is the arithmetic mean, and Sn is the n-th power of the geometric mean.
