List questions from hensels-lemma

115

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If $y$ is a $k$th power modulo $p^\gamma$, then it is also a $k$th power modulo $p^t$ for $t \geqslant \gamma$

Published on 14 Feb 2020 - 7:50

75

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Let $f(x)=x^3+x^2-5$. Show that for $n=1, 2,3, ...$ there is a unique $x_n$ modulo $7^n$ such that $f(x_n)\equiv 0\pmod{7^n}$.

Published on 23 Feb 2026 - 10:06

45

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Hensel's Lemma in $\mathbb{C} (\!( s )\!)$

Published on 18 Mar 2020 - 10:30

379

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Square roots in $\mathbb Z_p$

Published on 22 Mar 2020 - 1:38

27

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Finite ring extension

Published on 27 Mar 2020 - 10:21

69

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What is the $p$-adic density of irreducible polynomials congruent to $g(x)^n$ modulo $p$?

Published on 30 Mar 2020 - 3:58

292

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Application of Hensel's lemma $x^2 \equiv a (\mod 2^L)$

Published on 07 Apr 2020 - 14:08

230

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Find the number of incongruent solutions

Published on 17 May 2020 - 13:25

46

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Show that the sequence constructed in the proof for Hensel's lemma is Cauchy.

Published on 19 Jun 2020 - 14:24

59

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Questions about Hensel's lemma.

Published on 21 Jun 2020 - 16:53

2.5k

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Intuition for geometric definition of Henselian (local) scheme?

Published on 23 Aug 2016 - 12:57

242

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Lifting point on Curve

Published on 10 Oct 2016 - 7:27

94

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Tonelli and Hensel Lemma

Published on 10 Nov 2016 - 4:54

825

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How to use Hensel lemma to show that primitive root mod $p$ gives primitive root mod $p^2$ of the form $g + tp$

Published on 02 Dec 2016 - 20:07

137

Views

When can an algebraic number be approximated by a $p$-adic number?

Published on 03 Dec 2016 - 17:23

List Question

If $y$ is a $k$th power modulo $p^\gamma$, then it is also a $k$th power modulo $p^t$ for $t \geqslant \gamma$

Let $f(x)=x^3+x^2-5$. Show that for $n=1, 2,3, ...$ there is a unique $x_n$ modulo $7^n$ such that $f(x_n)\equiv 0\pmod{7^n}$.

Hensel's Lemma in $\mathbb{C} (\!( s )\!)$

Square roots in $\mathbb Z_p$

Finite ring extension

What is the $p$-adic density of irreducible polynomials congruent to $g(x)^n$ modulo $p$?

Application of Hensel's lemma $x^2 \equiv a (\mod 2^L)$

Find the number of incongruent solutions

Show that the sequence constructed in the proof for Hensel's lemma is Cauchy.

Questions about Hensel's lemma.

Intuition for geometric definition of Henselian (local) scheme?

Lifting point on Curve

Tonelli and Hensel Lemma

How to use Hensel lemma to show that primitive root mod $p$ gives primitive root mod $p^2$ of the form $g + tp$

When can an algebraic number be approximated by a $p$-adic number?

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