List questions from symmetric-polynomials

Published on 26 Mar 2026 - 16:07

108

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Find $f(a,b,c),g(a,b,c)\geqslant 0$ so that $7abc-\sum ab(a+b)= f ( a, b, c )+ ( \,a- b \, ) \cdot g ( a, b, c)$

Published on 27 Mar 2026 - 8:46

159

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Proving $6(x^3+y^3+z^3)^2 \leq (x^2+y^2+z^2)^3$, where $x+y+z=0$

Published on 07 Sep 2020 - 16:20

72

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Multivariate symmetric polynomial system

Published on 09 Sep 2020 - 16:14

74

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Inequality with a, b, c about finding minimal and maximal value

Published on 27 Mar 2026 - 2:39

144

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Finding all real $(a,b,c)$ satisfying $a+b+c=\frac1{a}+\frac1{b}+\frac1{c}$ and $a^2+b^2+c^2=\frac1{a^2}+\frac1{b^2}+\frac1{c^2}$

Published on 11 Sep 2020 - 16:02

137

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prove that $\sum_{cyc}\frac{a(b^2+c^2)}{a^2+bc}\ge 3$

Published on 26 Mar 2026 - 19:11

351

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Minimize $(x+y)(y+z)(z+x)$ given $xyz(x+y+z) = 1$

Published on 26 Mar 2026 - 17:34

106

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Symmetric inequality over 3 variables with restriction $a+b+c=1$

Published on 26 Mar 2026 - 23:09

90

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Express the weighted power sums

Published on 28 Sep 2020 - 18:07

88

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Prove that $\Sigma a_\nu = \Sigma b_\nu$ (Remmert, exercise 2, section 1 chapter 0)

Published on 29 Sep 2020 - 21:14

88

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Schur-Positivity of a simple polynomial

Published on 23 Feb 2026 - 23:30

164

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Inequality about elementary symmetric function

Published on 05 Oct 2020 - 3:59

112

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prove $\sum_{cyc}\frac{a^2}{a+2b^2}\ge 1$

Published on 06 Oct 2020 - 8:01

201

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prove that $\sum_{cyc}\frac{a}{b^2+c^2}\ge \frac{4}{5}\sum_{cyc}\frac{1}{b+c}$

Published on 26 Mar 2026 - 21:10

List Question

Proving $(a+b+c) \Big(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\Big) \leqslant 25$

Find $f(a,b,c),g(a,b,c)\geqslant 0$ so that $7abc-\sum ab(a+b)= f ( a, b, c )+ ( \,a- b \, ) \cdot g ( a, b, c)$

Proving $6(x^3+y^3+z^3)^2 \leq (x^2+y^2+z^2)^3$, where $x+y+z=0$

Multivariate symmetric polynomial system

Inequality with a, b, c about finding minimal and maximal value

Finding all real $(a,b,c)$ satisfying $a+b+c=\frac1{a}+\frac1{b}+\frac1{c}$ and $a^2+b^2+c^2=\frac1{a^2}+\frac1{b^2}+\frac1{c^2}$

prove that $\sum_{cyc}\frac{a(b^2+c^2)}{a^2+bc}\ge 3$

Minimize $(x+y)(y+z)(z+x)$ given $xyz(x+y+z) = 1$

Symmetric inequality over 3 variables with restriction $a+b+c=1$

Express the weighted power sums

Prove that $\Sigma a_\nu = \Sigma b_\nu$ (Remmert, exercise 2, section 1 chapter 0)

Schur-Positivity of a simple polynomial

Inequality about elementary symmetric function

prove $\sum_{cyc}\frac{a^2}{a+2b^2}\ge 1$

prove that $\sum_{cyc}\frac{a}{b^2+c^2}\ge \frac{4}{5}\sum_{cyc}\frac{1}{b+c}$

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