List questions from irreducible-polynomials

Published on 05 May 2026 - 8:19

69

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$\sqrt{3} \notin \mathbb{Q}(i)$

Published on 16 Apr 2026 - 1:07

105

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Show that $x^n + ax + p$ is irreducible, $p$ prime, $a \in \mathbb Z, \lvert a \rvert < p - 1$

Published on 15 Apr 2026 - 4:19

181

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ireducible polynomials with coefficients in $\{0,-1\}$

Published on 05 May 2026 - 7:34

106

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Irreducibility of $P(X)-P(Y)+1$

Published on 16 Apr 2026 - 6:15

485

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Closed algebraic form of $\cos(\frac{\pi}{7})$

Published on 13 Apr 2026 - 7:22

1k

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How do you call an element that is non-zero non-unit

Published on 12 Apr 2026 - 20:35

216

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Show that a polynomial is irreducible using Galois

Published on 13 Apr 2026 - 11:13

797

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Constructing a finite field of order 343.

Published on 10 May 2026 - 14:56

393

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Fastest method to verify $x^4-2x^2+9$ is irreducible so minimal

Published on 16 Apr 2026 - 15:50

64

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Are these statements about reducible polynomials correct?

Published on 11 Apr 2026 - 17:41

117

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Which field has the property that there is an irreducible polynomial of any degree over it?

Published on 10 May 2026 - 15:47

161

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Is there a ring R for which R[x] contains only finitely many irreducible monic polynomials?

Published on 13 Apr 2026 - 17:29

464

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Hessian of a smooth homogeneous polynomial of degree $d \ge 3$ is homogeneous of degree $3(d-2)$?

Published on 16 Apr 2026 - 15:01

112

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Proving irreducibility of polynomials over the rational numbers.

Published on 13 Apr 2026 - 4:17

List Question

Using Eisenstein's Criterion on something besides an integer

$\sqrt{3} \notin \mathbb{Q}(i)$

Show that $x^n + ax + p$ is irreducible, $p$ prime, $a \in \mathbb Z, \lvert a \rvert < p - 1$

ireducible polynomials with coefficients in $\{0,-1\}$

Irreducibility of $P(X)-P(Y)+1$

Closed algebraic form of $\cos(\frac{\pi}{7})$

How do you call an element that is non-zero non-unit

Show that a polynomial is irreducible using Galois

Constructing a finite field of order 343.

Fastest method to verify $x^4-2x^2+9$ is irreducible so minimal

Are these statements about reducible polynomials correct?

Which field has the property that there is an irreducible polynomial of any degree over it?

Is there a ring R for which R[x] contains only finitely many irreducible monic polynomials?

Hessian of a smooth homogeneous polynomial of degree $d \ge 3$ is homogeneous of degree $3(d-2)$?

Proving irreducibility of polynomials over the rational numbers.

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