List questions from symmetric-polynomials

Published on 29 Mar 2014 - 14:28

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if $abc=1$, then $a^2+b^2+c^2\ge a+b+c$

Published on 25 Mar 2026 - 7:43

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Proving AM-GM via $n \cdot (a_1^n + a_2^n + \dots + a_n^n) \ge (a_1^{n-1} + a_2^{n-1} + \dots + a_n^{n-1}) \cdot (a_1 + a_2 + \dots + a_n)$

Published on 25 Mar 2026 - 7:46

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Calculate the inequality

Published on 26 Mar 2026 - 3:10

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Prove or disprove the system about $n$th power has only one solution $x=y=1$

Published on 04 May 2014 - 1:35

119

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Non-symmetric polynomials, game

Published on 15 May 2014 - 14:53

89

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Equation on $\mathbb{R}$ : $(x+y+z)^3=x^3+y^3+z^3$

Published on 15 May 2014 - 23:04

795

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Specializations of elementary symmetric polynomials

Published on 19 May 2014 - 10:59

836

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If $f$ is an anti-symmetric polynomial, then $f=g\prod_{1\leq i < j\leq n}(X_i-X_j)$ for some $g$ symmetric

Published on 22 May 2014 - 10:50

120

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Let $a,b,c>0$ such $ \frac{b+c}{a}+ \frac{c+a}{b}+ \frac{a+b}{c} = 2\left(\frac{1}{ab}+\frac{1}{bc}+\frac{1}{ac} \right)$

Published on 25 Mar 2026 - 7:45

306

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An elementary symmetric polynomial question

Published on 29 May 2014 - 0:03

54

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Using elementary polynomials to solve system of linear polynomials

Published on 29 May 2014 - 15:12

833

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Generalizing Newton's identities: Trace formula for Schur functors

Published on 07 Jun 2014 - 3:14

1.2k

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Derivation and application of Newton's identity

Published on 15 Jun 2014 - 19:29

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Proving Newton's identities

Published on 23 Jun 2014 - 12:07

List Question

Constructing expressions

if $abc=1$, then $a^2+b^2+c^2\ge a+b+c$

Proving AM-GM via $n \cdot (a_1^n + a_2^n + \dots + a_n^n) \ge (a_1^{n-1} + a_2^{n-1} + \dots + a_n^{n-1}) \cdot (a_1 + a_2 + \dots + a_n)$

Calculate the inequality

Prove or disprove the system about $n$th power has only one solution $x=y=1$

Non-symmetric polynomials, game

Equation on $\mathbb{R}$ : $(x+y+z)^3=x^3+y^3+z^3$

Specializations of elementary symmetric polynomials

If $f$ is an anti-symmetric polynomial, then $f=g\prod_{1\leq i < j\leq n}(X_i-X_j)$ for some $g$ symmetric

Let $a,b,c>0$ such $ \frac{b+c}{a}+ \frac{c+a}{b}+ \frac{a+b}{c} = 2\left(\frac{1}{ab}+\frac{1}{bc}+\frac{1}{ac} \right)$

An elementary symmetric polynomial question

Using elementary polynomials to solve system of linear polynomials

Generalizing Newton's identities: Trace formula for Schur functors

Derivation and application of Newton's identity

Proving Newton's identities

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