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Solving Complex Number Equation with Galois theory

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#abstract-algebra #systems-of-equations #symmetric-polynomials
3k
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Symmetric Expressions in Quadratic Equation

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#algebra-precalculus #polynomials #quadratics #symmetric-polynomials #symmetric-functions
114
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General techniques for proving coefficients of a multinomial are all positive

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#real-analysis #algebraic-geometry #polynomials #symmetric-polynomials #real-algebraic-geometry
333
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Prove $x^n(y-z) + y^n(z-x) + z^n(x-y)$ is divisible by $(y-z)(z-x)(x-y)$

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#polynomials #symmetric-polynomials
532
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$\;32\displaystyle\left(\sum_{c}\frac{1}{7+(x-3)^2}\right)\leq \sum_{c} \frac{x^2+yz}{y+z}+6$

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#inequality #proof-explanation #fractions #symmetric-polynomials #sum-of-squares-method
209
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Solving 6 equations

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#systems-of-equations #quadratics #symmetric-polynomials
45
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Evaluating an elementry symmetric polynomial at some specific points.

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#polynomials #algorithms #computational-complexity #symmetric-polynomials
982
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Elementary Symmetric Polynomials and Determinant

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#linear-algebra #abstract-algebra #galois-theory #symmetric-polynomials
69
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Expansion of Elementary Symmetric Functions

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#combinatorics #reference-request #generating-functions #symmetric-polynomials
677
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Find the smallest and highest value of the product $xyz$

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#algebra-precalculus #inequality #systems-of-equations #cubics #symmetric-polynomials
117
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Show that for positive numbers a,b,c,d, $\sum_{cyc} ab \leq \frac{1}{4}\left(\sum_{cyc} a \right)^2$ and ...

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#inequality #summation #symmetric-polynomials #a.m.-g.m.-inequality
346
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Prove the inequality using Chebyshev's Inequality

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#algebra-precalculus #inequality #symmetric-polynomials #holder-inequality #rearrangement-inequality
125
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How to prove this inequality using AM-GM?

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#algebra-precalculus #inequality #products #symmetric-polynomials #a.m.-g.m.-inequality
56
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Existence of full set of $k$-th roots of unity in $GF(p)$

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#integers #roots-of-unity #symmetric-polynomials #unique-factorization-domains
74
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Whence Catalan's identity?

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#symmetric-polynomials #multivariate-polynomial

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