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How can I construct polynomials with "small" coefficients generating a prime "late"?

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#number-theory #elementary-number-theory #polynomials #prime-numbers #irreducible-polynomials
210
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Irreducibility of $x^5-9$

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#abstract-algebra #irreducible-polynomials
143
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How to prove $x^5 + y^7 +11$ irreducible in $\mathbb{Z}[x,y]$

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#ring-theory #irreducible-polynomials
42
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Quickest way to prove irreduciblity?

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#field-theory #finite-fields #extension-field #irreducible-polynomials
5.6k
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Find all irreducible polynomials of degrees $2$ and $3$ in $\Bbb{Z}_{2}[x]$.

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#abstract-algebra #ring-theory #irreducible-polynomials #polynomial-rings
74
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How does one prove that $(x^4 - 5)$ and $(x^4 + 5)$ are irreducible over $\mathbb{Q}$?

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#abstract-algebra #polynomials #irreducible-polynomials
230
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In $Z_5[x]$ , find all monic divisors of degree two for $2x^2+4x^3+3x^3+2x+4$

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#abstract-algebra #polynomials #ring-theory #irreducible-polynomials
52
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Construct field $\mathbb{Q}(\alpha)$

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#field-theory #irreducible-polynomials
1.1k
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Which roots of irreducible quartic polynomials are constructible by compass and straightedge?

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#galois-theory #irreducible-polynomials #geometric-construction
65
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Prove that $p(x)$ has no integer zeros.

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#irreducible-polynomials
1.2k
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Determine and construct irreducible polynomial (of degree >3) over finite fields.

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#abstract-algebra #number-theory #polynomials #irreducible-polynomials
66
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Irreducibility in Function Fields

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#irreducible-polynomials #function-fields
106
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Real roots of cubic polynomial

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#abstract-algebra #field-theory #irreducible-polynomials
86
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Degree of an extension field

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#finite-fields #extension-field #irreducible-polynomials #galois-extensions
40
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Irreducibility Prime Numbers Field Theory

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#abstract-algebra #irreducible-polynomials

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