Question

How to prove $(a-b)^3 + (b-c)^3 + (c-a)^3 -3(a-b)(b-c)(c-a) = 0$ without calculations

score 6.3k · Answer 1 · 2013-06-07 10:50:53

6.3k

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How to prove $(a-b)^3 + (b-c)^3 + (c-a)^3 -3(a-b)(b-c)(c-a) = 0$ without calculations

Published on 07 Jun 2013 - 10:50

score 45 · Answer 2 · 2013-06-12 17:42:00

45

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signature of pseudo-Riemannian metric made of Newton polynomials

Published on 12 Jun 2013 - 17:42

score 673 · Answer 3 · 2013-06-14 17:58:50

What is the function space generated by addition and $(a,b)\mapsto (a+b)^{-1}\cdot a\cdot b$ of elements and their inverses?

score 166 · Answer 4 · 2026-03-26 10:45:13

166

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Expansions of symmetric polynomials in terms of Jack symmetric polynomials

Published on 26 Mar 2026 - 10:45

score 113 · Answer 5 · 2013-06-27 23:50:53

113

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symmetric polynomial inequality?

Published on 27 Jun 2013 - 23:50

score 262 · Answer 6 · 2026-03-30 06:48:42

262

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If $abc=1$ and $\prod_{\text{cyc}}(a^2+b^2)=8$, then $(a+b+c)^3\prod_{\text{cyc}}(a^2+b^2)\ge\left (\sum_{\operatorname{cyc}} (a^2b+b^2a) \right) ^3$.

Published on 30 Mar 2026 - 6:48

score 118 · Answer 7 · 2013-07-03 06:22:05

118

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Some lemma on elementary symmetric polynomial

Published on 03 Jul 2013 - 6:22

score 1.2k · Answer 8 · 2013-07-09 12:35:30

1.2k

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are elementary symmetric polynomials concave on probability distributions?

Published on 09 Jul 2013 - 12:35

score 112 · Answer 9 · 2013-07-18 22:05:59

112

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Is there a subgroup of $S_{10}$ having $5040$ elements other than $S_7$?

Published on 18 Jul 2013 - 22:05

score 149 · Answer 10 · 2013-07-20 08:57:24

149

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If $x,y,z \in \Bbb{R}$ such that $x+y+z=4$ and $x^2+y^2+z^2=6$, then show that $x,y,z \in [2/3,2]$.

Published on 20 Jul 2013 - 8:57

score 82 · Answer 11 · 2013-07-25 02:26:12

82

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Clarification on proof including symmetric polynomials

Published on 25 Jul 2013 - 2:26

score 1.1k · Answer 12 · 2013-07-25 23:32:17

1.1k

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Symmetric polynomials

Published on 25 Jul 2013 - 23:32

score 73 · Answer 13 · 2013-07-29 21:45:59

73

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Factoring the group action on $\prod X_k^k $ gives another group?

Published on 29 Jul 2013 - 21:45

score 3.8k · Answer 14 · 2026-03-27 10:31:32

3.8k

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Explain the terms : homogeneous , symmetric , anti-symmetric , cyclic with respect to polynomials.

Published on 27 Mar 2026 - 10:31

score 6.2k · Answer 15 · 2013-08-18 17:47:17

Find the value of $\textrm{cosec}^2\left(\frac\pi7\right) +\textrm{cosec}^2\left(\frac{2\pi}7\right)+\textrm{cosec}^2\left(\frac{4\pi}7\right)$

List Question

How to prove $(a-b)^3 + (b-c)^3 + (c-a)^3 -3(a-b)(b-c)(c-a) = 0$ without calculations

signature of pseudo-Riemannian metric made of Newton polynomials

What is the function space generated by addition and $(a,b)\mapsto (a+b)^{-1}\cdot a\cdot b$ of elements and their inverses?

Expansions of symmetric polynomials in terms of Jack symmetric polynomials

symmetric polynomial inequality?

If $abc=1$ and $\prod_{\text{cyc}}(a^2+b^2)=8$, then $(a+b+c)^3\prod_{\text{cyc}}(a^2+b^2)\ge\left (\sum_{\operatorname{cyc}} (a^2b+b^2a) \right) ^3$.

Some lemma on elementary symmetric polynomial

are elementary symmetric polynomials concave on probability distributions?

Is there a subgroup of $S_{10}$ having $5040$ elements other than $S_7$?

If $x,y,z \in \Bbb{R}$ such that $x+y+z=4$ and $x^2+y^2+z^2=6$, then show that $x,y,z \in [2/3,2]$.

Clarification on proof including symmetric polynomials

Symmetric polynomials

Factoring the group action on $\prod X_k^k $ gives another group?

Explain the terms : homogeneous , symmetric , anti-symmetric , cyclic with respect to polynomials.

Find the value of $\textrm{cosec}^2\left(\frac\pi7\right) +\textrm{cosec}^2\left(\frac{2\pi}7\right)+\textrm{cosec}^2\left(\frac{4\pi}7\right)$

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