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$(a+b-c)(b+c-a)(c+a-b) \leq abc$

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#inequality #polynomials #contest-math #symmetric-polynomials
79
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Find a + b + c + bc.

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#systems-of-equations #quadratics #symmetric-polynomials
55
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A cyclic inequality

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#algebra-precalculus #inequality #symmetric-polynomials
51
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Find double summation

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#polynomials #summation #roots-of-unity #symmetric-polynomials
188
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Prove that $\sum_{cyc}\frac{1}{(2a+2b+c)^3}\le\frac{3}{125x}$ if $abc=x$

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#inequality #fractions #symmetric-polynomials #a.m.-g.m.-inequality #cauchy-schwarz-inequality
140
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Equation System with 3 variables

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#systems-of-equations #symmetric-polynomials
212
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Prove $x+y+z\geq3$ given $xyz=1$ and $0<x,y,z\in\mathbb{F}$

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#abstract-algebra #inequality #field-theory #symmetric-polynomials
72
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System of simultaneous equations $x^n+y^n+z^n=3$ ($n$=1,2,5)

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#systems-of-equations #symmetric-polynomials
201
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Is a polynomial in two variables of degree three, a symmetric element w.r.t. some involution?

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#algebraic-geometry #polynomials #commutative-algebra #symmetric-polynomials
85
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On the construction of Soergel bimodules

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#polynomials #representation-theory #lie-algebras #symmetric-groups #symmetric-polynomials
81
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Indecomposable Soergel bimodules for $S_3$

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#representation-theory #lie-algebras #symmetric-groups #symmetric-polynomials
190
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Solving a system of equations $(x+y-z=1), (x^2+y^2-z^2=5-2xy), (x^3+y^3-z^3=43-3xy)$

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#systems-of-equations #cubics #symmetric-polynomials
77
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Show: $n(x-y)y^{n-1} < x^n-y^n < n(x-y)x^{n-1}$

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#inequality #summation #symmetric-polynomials
281
Views

Factors of a symmetric polynomial

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#abstract-algebra #field-theory #symmetric-polynomials
52
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An atypical inequality

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#inequality #polynomials #symmetric-polynomials #a.m.-g.m.-inequality

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