Schur's inequality
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This article is about the algebraic inequality in 3 variables. For the integral inequality, see Schur test.
In mathematics, Schur's inequality, named after Issai Schur, establishes that for all non-negative real numbers x, y, z, and t>0,
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with equality if and only if x = y = z or two of them are equal and the other is zero. When t is an even positive integer, the inequality holds for all real numbers x, y and z.
When , the following well-known special case can be derived: