List questions from finite-fields

Published on 20 Oct 2019 - 22:57

337

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Prove that $x^3+2y^3+4z^3\equiv6xyz \pmod{7} \Rightarrow x\equiv y\equiv z\equiv 0 \pmod{7}$

Published on 20 Oct 2019 - 23:48

48

Views

Exponentiation of a modulo sum

Published on 30 Mar 2026 - 8:41

78

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$W$ is $\sigma$-invariant i.e., $\sigma(W) \subset W$ implies that $W$ has a basis consisting of elements of $\mathbb F_{q}^n.$

Published on 24 Oct 2019 - 12:57

1.1k

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Row reducing matrix over a finite field

Published on 26 Mar 2026 - 2:53

255

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How to prove $(\phi-1)(\phi-2)...(\phi-p) = \sqrt{5} + p\left(\frac{1}{2}+A\sqrt{5}\right) \bmod p^2$?

Published on 26 Mar 2026 - 21:09

970

Views

Binomial coefficients modulo a prime

Published on 28 Oct 2019 - 4:43

49

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Relation between polynomials $f$ and $g$ such that roots of $g$ are squares of roots of $f$.

Published on 29 Mar 2026 - 8:45

32

Views

Minimal number of nonzero points in $\mathbb{F}_2^n$ which cover all subspaces of codimension k

Published on 25 Mar 2026 - 11:06

20

Views

Comfirmation of Existence of finite field

Published on 29 Oct 2019 - 13:59

139

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Prove $\sum_{\gcd(p,1+i-i^2)=1} \frac{i}{1+i-i^2} = -5^{(p-3)/2} \bmod p$

Published on 28 Mar 2026 - 9:57

79

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Triples in the field with 9 elements

Published on 30 Oct 2019 - 23:23

423

Views

Number of invertible elements in quotient ring

Published on 01 Nov 2019 - 1:14

1.4k

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Show that $x^6+x^3+1$ is irreducible over $\mathbb{F}_2$

Published on 29 Mar 2026 - 10:18

209

Views

Set of Matrices Over Finite Field Whose Pairwise Differences are Invertible

Published on 28 Mar 2026 - 8:49

List Question

Multiplicative order of element in field extension

Prove that $x^3+2y^3+4z^3\equiv6xyz \pmod{7} \Rightarrow x\equiv y\equiv z\equiv 0 \pmod{7}$

Exponentiation of a modulo sum

$W$ is $\sigma$-invariant i.e., $\sigma(W) \subset W$ implies that $W$ has a basis consisting of elements of $\mathbb F_{q}^n.$

Row reducing matrix over a finite field

How to prove $(\phi-1)(\phi-2)...(\phi-p) = \sqrt{5} + p\left(\frac{1}{2}+A\sqrt{5}\right) \bmod p^2$?

Binomial coefficients modulo a prime

Relation between polynomials $f$ and $g$ such that roots of $g$ are squares of roots of $f$.

Minimal number of nonzero points in $\mathbb{F}_2^n$ which cover all subspaces of codimension k

Comfirmation of Existence of finite field

Prove $\sum_{\gcd(p,1+i-i^2)=1} \frac{i}{1+i-i^2} = -5^{(p-3)/2} \bmod p$

Triples in the field with 9 elements

Number of invertible elements in quotient ring

Show that $x^6+x^3+1$ is irreducible over $\mathbb{F}_2$

Set of Matrices Over Finite Field Whose Pairwise Differences are Invertible

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