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Geometric inequality involving sides of the triangle

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#inequality #triangles #symmetric-polynomials #a.m.-g.m.-inequality #geometric-inequalities
74
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Find the value of $\frac{1}{a^3}+\frac{1}{b^3}$

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#algebra-precalculus #polynomials #roots #quadratics #symmetric-polynomials
445
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Almost-invariant polynomials under dihedral group action

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#abstract-algebra #commutative-algebra #representation-theory #symmetric-polynomials #invariant-theory
162
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What are the one-dimensional elements in the ring of symmetric functions?

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#abstract-algebra #symmetric-polynomials
139
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How to solve this equation algebraically

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#systems-of-equations #symmetric-polynomials
229
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Polynomials with $S_n \times \mathbb{Z}_2$ symmetry

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#polynomials #representation-theory #symmetric-polynomials #invariant-theory
120
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Symmetrized monomials under Weyl group?

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#symmetric-groups #symmetric-polynomials #symmetric-functions
180
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Prove $(a+b)^3(b+c)^3(c+d)^3(d+a)^3\ge 16a^2b^2c^2d^2$

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#multivariable-calculus #inequality #substitution #symmetric-polynomials #uvw
166
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Integer divisibility

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#combinatorics #elementary-number-theory #divisibility #integers #symmetric-polynomials
112
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Product as the sum of powers times a symmetric polynomial: What's the name of this property and what is it used for?

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#products #symmetric-polynomials
77
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Is $S_i(1,2,\dots,p-2) \equiv 1 \pmod{p}$ for all values of $i$ whenever $p$ is prime?

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#prime-numbers #factorial #congruences #symmetric-polynomials
122
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System of equations symmetric

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#systems-of-equations #symmetric-polynomials
401
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Symmetric system of $3$ equations: $x+y+z=23$, $xy+yz+xz=144$, $xyz=252$

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#algebra-precalculus #systems-of-equations #symmetric-polynomials
667
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Symmetric roots of polynomial

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#roots #symmetric-polynomials
686
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How to decide if a polynomial is symmetric?

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#abstract-algebra #polynomials #symmetric-polynomials

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