Question

Every field with characterisitic $p$ contains the field $\mathbb{Z}_p$

score 751 · Answer 1 · 2014-08-08 13:26:28

751

Views

Every field with characterisitic $p$ contains the field $\mathbb{Z}_p$

Published on 08 Aug 2014 - 13:26

score 85 · Answer 2 · 2014-08-08 20:28:38

85

Views

order of $x \operatorname{mod} p(x)$ in $\mathbb Z_2$

Published on 08 Aug 2014 - 20:28

score 1k · Answer 3 · 2026-03-26 04:53:20

1k

Views

Automorphisms of splitting field of $x^p-x-a$

Published on 26 Mar 2026 - 4:53

score 1.7k · Answer 4 · 2026-03-25 23:36:05

1.7k

Views

How does Mathematica solve $f(x)\equiv 0\pmod p$?

Published on 25 Mar 2026 - 23:36

score 1.2k · Answer 5 · 2014-08-12 03:15:07

1.2k

Views

Inclusion of Fields whose order is a prime power

Published on 12 Aug 2014 - 3:15

score 96 · Answer 6 · 2014-08-19 16:44:59

96

Views

Showing the existence of sub fields of a finite field

Published on 19 Aug 2014 - 16:44

score 24 · Answer 7 · 2014-08-20 05:18:29

24

Views

find an example for an equation in finite field

Published on 20 Aug 2014 - 5:18

score 299 · Answer 8 · 2026-03-25 10:15:35

299

Views

Simplify exponential sum over $\mathbb{F}_p$ to prove identity

Published on 25 Mar 2026 - 10:15

score 300 · Answer 9 · 2026-03-26 06:30:50

300

Views

Counting the roots of a polynomial over a finite field

Published on 26 Mar 2026 - 6:30

score 492 · Answer 10 · 2026-02-23 04:55:06

492

Views

Why is $1 + 1 = 0$ in $\{0, 1\}$ (binary field) and not 1 or 2?

Published on 23 Feb 2026 - 4:55

score 1.6k · Answer 11 · 2014-08-21 18:50:18

1.6k

Views

Every irreducible polynomial of degree $m$ over $\mathbb F_p$ divides $x^{p^m}-x$

Published on 21 Aug 2014 - 18:50

score 94 · Answer 12 · 2014-08-21 20:55:55

94

Views

Presence of non square elements in $GF(p)$

Published on 21 Aug 2014 - 20:55

score 1.1k · Answer 13 · 2014-08-21 23:18:42

1.1k

Views

Proving that either $x $ or $2x$ is a generator of the cyclic group $(\mathbb Z_3[x]/\langle f(x) \rangle)^*$

Published on 21 Aug 2014 - 23:18

score 154 · Answer 14 · 2014-08-23 15:42:16

154

Views

Show that if $\mathrm{Tr}(y)=0$ then there exists a $x$ such that $x^p-x=y$.

Published on 23 Aug 2014 - 15:42

score 154 · Answer 15 · 2014-08-24 14:05:13

154

Views

Prove the number of unordered pairs of linearly independent elements

Published on 24 Aug 2014 - 14:05

List Question

Every field with characterisitic $p$ contains the field $\mathbb{Z}_p$

order of $x \operatorname{mod} p(x)$ in $\mathbb Z_2$

Automorphisms of splitting field of $x^p-x-a$

How does Mathematica solve $f(x)\equiv 0\pmod p$?

Inclusion of Fields whose order is a prime power

Showing the existence of sub fields of a finite field

find an example for an equation in finite field

Simplify exponential sum over $\mathbb{F}_p$ to prove identity

Counting the roots of a polynomial over a finite field

Why is $1 + 1 = 0$ in $\{0, 1\}$ (binary field) and not 1 or 2?

Every irreducible polynomial of degree $m$ over $\mathbb F_p$ divides $x^{p^m}-x$

Presence of non square elements in $GF(p)$

Proving that either $x $ or $2x$ is a generator of the cyclic group $(\mathbb Z_3[x]/\langle f(x) \rangle)^*$

Show that if $\mathrm{Tr}(y)=0$ then there exists a $x$ such that $x^p-x=y$.

Prove the number of unordered pairs of linearly independent elements

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