List questions from hensels-lemma

Published on 31 Jan 2017 - 7:59

157

Views

Computing $m^n (mod\,p^2)$ efficiently for a large prime $p$

Published on 06 Apr 2017 - 19:51

162

Views

Applying Hensel's lemma to solve $x^2 + 8 \equiv 0\pmod {121}$.

Published on 25 Feb 2023 - 0:24

70

Views

Ring isomorphism via Hensel lifting

Published on 13 Mar 2023 - 12:13

109

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Let $K$ be a number field and $v$ be its place. Let $K_v$ be completion of $K$ at $v$. I want to prove $y^2=x^4-p$ has $K_v$ rational point.

Published on 04 Apr 2023 - 17:41

120

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Find prime number which satisfies $p \in {\Bbb{{Q}_2}^{\times}}^2-{{\Bbb{Q}_2}^{\times}}^4$

Published on 16 Apr 2023 - 14:44

62

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Connection between roots in $Q_p$ and $Z_p$

Published on 04 Jun 2023 - 9:38

72

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How often is a monic polynomial highly divisible by p?

Published on 11 Jun 2023 - 16:34

59

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Number of solutions to system of polynomial equations $\!\bmod p^k$

Published on 03 Aug 2023 - 21:55

21

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Analytic parameterization of a residue disk

Published on 06 Sep 2023 - 15:10

76

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A generalization of Hensel lemma

Published on 07 Nov 2023 - 17:00

27

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What's a direct or quickest proof of simple zeros lift to factorizations lift?

Published on 26 Nov 2023 - 22:53

149

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Proof of Hensel's Lemma not clear

Published on 22 Jan 2015 - 2:49

162

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Idea of Hensel's Lemma

Published on 29 Jan 2015 - 15:06

1.5k

Views

There is a primitive $m^{th}$ root of unity in $\mathbb{Q}_p$ $\Leftrightarrow m \mid (p-1)$

Published on 29 Jan 2015 - 16:45

List Question

Deducing Hensel's lemma for polynomials

Computing $m^n (mod\,p^2)$ efficiently for a large prime $p$

Applying Hensel's lemma to solve $x^2 + 8 \equiv 0\pmod {121}$.

Ring isomorphism via Hensel lifting

Let $K$ be a number field and $v$ be its place. Let $K_v$ be completion of $K$ at $v$. I want to prove $y^2=x^4-p$ has $K_v$ rational point.

Find prime number which satisfies $p \in {\Bbb{{Q}_2}^{\times}}^2-{{\Bbb{Q}_2}^{\times}}^4$

Connection between roots in $Q_p$ and $Z_p$

How often is a monic polynomial highly divisible by p?

Number of solutions to system of polynomial equations $\!\bmod p^k$

Analytic parameterization of a residue disk

A generalization of Hensel lemma

What's a direct or quickest proof of simple zeros lift to factorizations lift?

Proof of Hensel's Lemma not clear

Idea of Hensel's Lemma

There is a primitive $m^{th}$ root of unity in $\mathbb{Q}_p$ $\Leftrightarrow m \mid (p-1)$

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