List questions from symmetric-polynomials

Published on 05 Apr 2020 - 8:44

1k

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For all real $x, y$ that satisfy $x^3+y^3=7$ and $x^2+y^2+x+y+xy=4$

Published on 05 Apr 2020 - 14:50

420

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Given a polynomial with roots $a, b, c, d, e$, find the polynomial whose roots are $abc, abd, abe, ...$

Published on 23 Feb 2026 - 6:36

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$\alpha,\beta,\gamma$ are the roots of the equation $x^3 − 9x + 9 = 0$. Find the value of $ \alpha^{-5}+\beta^{-5}+\gamma^{-5}$

Published on 06 Apr 2020 - 14:07

86

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Proving $abcd \le 3+ ab+ac+ad+bc+bd+cd$ when $(a^2+1)(b^2+1)(c^2+1)(d^2+1)=16$

Published on 27 Mar 2026 - 12:56

150

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If a,b,c be roots of $2x^3+x^2+x-1=0$ show that some expression is equal to 16.

Published on 08 Apr 2020 - 14:10

192

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For positive a,b,c,d, if $a^2+b^2+c^2+d^2+abcd=5$, show $a+b+c+d\leq 4$.

Published on 25 Mar 2026 - 9:39

144

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Proving $\sum\limits_{\rm cyc} 1/(a^2 -b+4) \geq3/4$

Published on 25 Mar 2026 - 9:37

224

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Expansion of $(a+b+c+d+e+....)^n$, but with all coefficients equal to 1.

Published on 26 Mar 2026 - 8:03

1.2k

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Symmetric rational function is a rational function in the elementary symmetric polynomials.

Published on 10 Apr 2020 - 13:00

705

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Symmetric functions written in terms of the elementary symmetric polynomials.

Published on 25 Mar 2026 - 17:40

105

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Find the minimum value of $a^2+b^2+c^2+2abc$ when $a+b+c=3$ and $a,b,c\geq0$.

Published on 26 Mar 2026 - 20:44

75

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Multinomial sum?

Published on 11 Apr 2020 - 15:54

40

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Is the plethysm of two polynomials the same as the substitution of one into another?

Published on 16 Apr 2020 - 2:50

92

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Can Weierstrass's theorem be specialized to symmetric functions and symmetric polynomials?

Published on 23 Feb 2026 - 4:56

List Question

Formula for some specific polynomials

For all real $x, y$ that satisfy $x^3+y^3=7$ and $x^2+y^2+x+y+xy=4$

Given a polynomial with roots $a, b, c, d, e$, find the polynomial whose roots are $abc, abd, abe, ...$

$\alpha,\beta,\gamma$ are the roots of the equation $x^3 − 9x + 9 = 0$. Find the value of $ \alpha^{-5}+\beta^{-5}+\gamma^{-5}$

Proving $abcd \le 3+ ab+ac+ad+bc+bd+cd$ when $(a^2+1)(b^2+1)(c^2+1)(d^2+1)=16$

If a,b,c be roots of $2x^3+x^2+x-1=0$ show that some expression is equal to 16.

For positive a,b,c,d, if $a^2+b^2+c^2+d^2+abcd=5$, show $a+b+c+d\leq 4$.

Proving $\sum\limits_{\rm cyc} 1/(a^2 -b+4) \geq3/4$

Expansion of $(a+b+c+d+e+....)^n$, but with all coefficients equal to 1.

Symmetric rational function is a rational function in the elementary symmetric polynomials.

Symmetric functions written in terms of the elementary symmetric polynomials.

Find the minimum value of $a^2+b^2+c^2+2abc$ when $a+b+c=3$ and $a,b,c\geq0$.

Multinomial sum?

Is the plethysm of two polynomials the same as the substitution of one into another?

Can Weierstrass's theorem be specialized to symmetric functions and symmetric polynomials?

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