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Partition the rationals with respect to a multivariate polynomial which sends classes to classes

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#abstract-algebra #number-theory #polynomials #dynamical-systems
976
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Dividing one polynomial by another

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#polynomials #fractions #euclidean-domain
68
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A sufficient condition for $x^p-x-a$ to be primitive

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#polynomials #finite-fields
71
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If $|a|\ge 2$,$|b|\ge 2$, $P(x)=x^4-(a+b)x^3+(ab+2) x^2-(a+b)x+1$, prove that all roots of $P(x)$ are real

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#polynomials #contest-math #roots
1.8k
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How to create the Smith Mcmillan form of a polynomial matrix?

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#matrices #polynomials #smith-normal-form
134
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Algebraic dependence is transitive

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#algebraic-geometry #polynomials
55
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Factor theorem applied to an "extreme" example

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#polynomials
146
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Reduction modulo $p$ of prime ideals

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#polynomials #commutative-algebra
53
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Adding a prime number to a special homogeneous prime ideal preserves primeness

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#polynomials #commutative-algebra #irreducible-polynomials #maximal-and-prime-ideals
167
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Ideas on proving or disproving a ring is integrally closed

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#abstract-algebra #polynomials #ring-theory #quotient-spaces #integral-extensions
660
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Prove all the roots of a given polynomial lie in the disk with radius $2$

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#complex-analysis #inequality #polynomials #complex-numbers #absolute-value
134
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Given a root, determine $a$ and $b$.

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#algebra-precalculus #polynomials #roots #cubics
176
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Prove that an element of a quotient ring of polynomials is algebraic

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#abstract-algebra #polynomials #field-theory
558
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Find the natural solutions of $a^3-b^3=999$

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#elementary-number-theory #polynomials #divisibility #diophantine-equations #integers
337
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Factorizing $x^4-13x^3+56x^2-19$

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#algebra-precalculus #polynomials #factoring

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