List questions from symmetric-polynomials

Published on 25 Mar 2026 - 21:44

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Inequality $\left(1-\frac{x(1-x)+y(1-y)}{1-x+1-y}\right)^2+(1-\frac{x+y}{2})^2\geq (1-x)^2+(1-y)^2$

Published on 31 Aug 2019 - 14:53

71

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Proving the inequality $4(a^6+b^6) \ge (a+b)(a^2+b^2)(a^3+b^3)$

Published on 02 Sep 2019 - 14:59

97

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$a, b, c$ are positives such that $a + b + c = 1$. Determine the maximal value of $\sum\limits_{cyc}\frac1{a(b + c)} - \frac{a^2 + b^2 + c^2}{2abc}$.

Published on 25 Mar 2026 - 9:29

1k

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Cubic diophantine equation with a prime $x^3 + y^3 + z^3 - 3xyz = p$.

Published on 25 Mar 2026 - 23:23

112

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Does this system of infinite equations has an (almost) unique solution?

Published on 12 Sep 2019 - 6:35

267

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A hard inequality indian olympiad problem

Published on 25 Mar 2026 - 6:09

2.9k

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What is $\alpha^{4} + \beta^{4} + \gamma^{4}$?

Published on 18 Sep 2019 - 3:23

66

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Non-trivial solution of $x_1^k+ \cdots + x_n^k =0$ for $k= 1, 2, \cdots, N$

Published on 18 Sep 2019 - 16:19

939

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Sum of Vandermonde determinant

Published on 24 Sep 2019 - 8:30

84

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Is this system of equations "solvable"?

Published on 01 Oct 2019 - 20:57

513

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Elementary Symmetric Polynomials, Roots of cubic polynomials

Published on 11 Mar 2014 - 21:40

162

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Unique "splitting fields" for infinite polynomials

Published on 11 Mar 2014 - 23:14

664

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Given six numbers $x,y,z,a,b,c$ which satisfy the following relations. Express $x+y+z$ in terms of $a,b,c$

Published on 22 Mar 2014 - 8:11

1.5k

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Express symmetric polynomial $\prod_{i < j} (X_i+X_j)$ in terms of elementary symmetric functions

Published on 24 Mar 2014 - 17:13

List Question

Lagrange System of Equations

Inequality $\left(1-\frac{x(1-x)+y(1-y)}{1-x+1-y}\right)^2+(1-\frac{x+y}{2})^2\geq (1-x)^2+(1-y)^2$

Proving the inequality $4(a^6+b^6) \ge (a+b)(a^2+b^2)(a^3+b^3)$

$a, b, c$ are positives such that $a + b + c = 1$. Determine the maximal value of $\sum\limits_{cyc}\frac1{a(b + c)} - \frac{a^2 + b^2 + c^2}{2abc}$.

Cubic diophantine equation with a prime $x^3 + y^3 + z^3 - 3xyz = p$.

Does this system of infinite equations has an (almost) unique solution?

A hard inequality indian olympiad problem

What is $\alpha^{4} + \beta^{4} + \gamma^{4}$?

Non-trivial solution of $x_1^k+ \cdots + x_n^k =0$ for $k= 1, 2, \cdots, N$

Sum of Vandermonde determinant

Is this system of equations "solvable"?

Elementary Symmetric Polynomials, Roots of cubic polynomials

Unique "splitting fields" for infinite polynomials

Given six numbers $x,y,z,a,b,c$ which satisfy the following relations. Express $x+y+z$ in terms of $a,b,c$

Express symmetric polynomial $\prod_{i < j} (X_i+X_j)$ in terms of elementary symmetric functions

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