List questions from symmetric-polynomials

Published on 17 Mar 2026 - 6:09

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show this $\prod(a^3+b^3+ab)^2\ge (\sum a^2b)^3( \sum ab^2)^3$

Published on 17 Mar 2026 - 16:00

185

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replacing Inequalities

Published on 16 Mar 2026 - 20:25

424

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show that amazing result $\frac{\sum a^7}{\sum a^5\sum a^2}=\frac{7}{10}$

Published on 04 May 2018 - 15:13

155

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Proving an inequality for elementary symmetric polynomials

Published on 06 May 2018 - 13:28

679

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Whenever $a+b+c=1$, $\frac{bc+a+1}{a^2+1} + \frac{ac+b+1}{b^2+1} + \frac{ab+c+1}{c^2+1} \le \frac{39}{10}$

Published on 25 Mar 2026 - 1:18

91

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Muirhead's inequality -- equality occur

Published on 20 Mar 2026 - 19:23

119

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Prove this stronger inequality

Published on 23 Mar 2026 - 10:50

250

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Galois group of symmetric polynomial extension

Published on 10 May 2018 - 11:45

94

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Eliminate $x,y,z$ from equations

Published on 14 May 2018 - 16:08

504

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USAMO 2018: Show that $2(ab+bc+ca) + 4 \min(a^2,b^2,c^2) \geq a^2 + b^2 + c^2$

Published on 16 May 2018 - 12:26

409

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solve the system of equation for $a,b,c,d,e$

Published on 16 May 2018 - 12:38

91

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For $a>0,b>0,c>0$, prove $\frac{a(a^2+bc)}{b+c}+\frac{b(b^2+ca)}{bc+a}+\frac{c(c^2+ab)}{a+b}\geq ab+bc+ca$

Published on 23 Mar 2026 - 3:25

119

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Question from a Moscow summer camp

Published on 22 Mar 2026 - 4:38

71

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Factoring a polynomial in short and simple way.

Published on 24 May 2018 - 18:37

List Question

Stronger than Nessbit

show this $\prod(a^3+b^3+ab)^2\ge (\sum a^2b)^3( \sum ab^2)^3$

replacing Inequalities

show that amazing result $\frac{\sum a^7}{\sum a^5\sum a^2}=\frac{7}{10}$

Proving an inequality for elementary symmetric polynomials

Whenever $a+b+c=1$, $\frac{bc+a+1}{a^2+1} + \frac{ac+b+1}{b^2+1} + \frac{ab+c+1}{c^2+1} \le \frac{39}{10}$

Muirhead's inequality -- equality occur

Prove this stronger inequality

Galois group of symmetric polynomial extension

Eliminate $x,y,z$ from equations

USAMO 2018: Show that $2(ab+bc+ca) + 4 \min(a^2,b^2,c^2) \geq a^2 + b^2 + c^2$

solve the system of equation for $a,b,c,d,e$

For $a>0,b>0,c>0$, prove $\frac{a(a^2+bc)}{b+c}+\frac{b(b^2+ca)}{bc+a}+\frac{c(c^2+ab)}{a+b}\geq ab+bc+ca$

Question from a Moscow summer camp

Factoring a polynomial in short and simple way.

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