List questions from hensels-lemma

Published on 25 Mar 2026 - 2:59

158

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

Published on 25 Mar 2026 - 2:59

163

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

Published on 25 Mar 2026 - 6:03

71

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Ring isomorphism via Hensel lifting

Published on 25 Mar 2026 - 2:59

110

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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 25 Mar 2026 - 3:04

121

Views

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

Published on 25 Mar 2026 - 3:03

63

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Connection between roots in $Q_p$ and $Z_p$

Published on 25 Mar 2026 - 3:01

73

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How often is a monic polynomial highly divisible by p?

Published on 25 Mar 2026 - 3:07

60

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

Published on 25 Mar 2026 - 3:02

22

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Analytic parameterization of a residue disk

Published on 25 Mar 2026 - 4:36

78

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A generalization of Hensel lemma

Published on 01 Apr 2026 - 11:11

28

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

Published on 25 Mar 2026 - 3:04

150

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Proof of Hensel's Lemma not clear

Published on 25 Mar 2026 - 3:02

164

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Idea of Hensel's Lemma

Published on 01 Apr 2026 - 8:00

1.5k

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

Published on 25 Mar 2026 - 3:07

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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