List questions from hensels-lemma

116

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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 25 Mar 2026 - 1:18

76

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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 09 Apr 2026 - 15:24

47

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

Published on 27 Mar 2026 - 14:48

382

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Square roots in $\mathbb Z_p$

Published on 10 Apr 2026 - 23:12

30

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Finite ring extension

Published on 10 Apr 2026 - 7:47

70

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

Published on 25 Mar 2026 - 1:20

293

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

Published on 25 Mar 2026 - 3:07

232

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Find the number of incongruent solutions

Published on 27 Mar 2026 - 14:21

47

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

Published on 25 Mar 2026 - 3:02

62

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Questions about Hensel's lemma.

Published on 10 Apr 2026 - 20:47

2.5k

Views

Intuition for geometric definition of Henselian (local) scheme?

Published on 25 Mar 2026 - 1:17

245

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Lifting point on Curve

Published on 10 Apr 2026 - 4:50

97

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Tonelli and Hensel Lemma

Published on 10 Apr 2026 - 17:50

826

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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 25 Mar 2026 - 1:18

138

Views

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

Published on 25 Mar 2026 - 4:38

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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