List questions from hensels-lemma

Published on 24 Mar 2016 - 12:21

45

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$/6 = 10 \pmod {7^2}$

Published on 25 Mar 2026 - 0:41

143

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Finding primitive root of unity using Newton iteration

Published on 15 Mar 2026 - 10:05

3.3k

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Coding Theory and Algebra

Published on 17 Apr 2013 - 13:46

451

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A $p$-adic unit is an $n^{th}$ power if it is congruent to a $n^{th}$ power mod $m$ (Eisenbud exercise)

Published on 27 Apr 2017 - 17:24

160

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Computing the quotient $\mathbb{Q}_p[x]/(x^2 + 1)$

Published on 02 May 2017 - 17:00

191

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square root of $-1$ in $\mathbb{Q}_p$

Published on 03 May 2017 - 22:42

322

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Squares in $\mathbb{Q}_p \bmod p$ (p-adic numbers)

Published on 04 May 2017 - 18:20

144

Views

$U/U_3 \equiv (\mathbb{Z}/27\mathbb{Z})^{\times}$

Published on 06 May 2017 - 4:55

641

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$\mathbb{Z}_p^*$ has a primitive $p - 1$-th root of unity (p-adic)

Published on 07 May 2017 - 17:30

84

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$\alpha \in \mathbb{Z}_p^{\times}$ iff there are infinitely many $n \in \mathbb{Z}_{>0}$ such that $X^n = \alpha$ has a solution.

Published on 01 Jun 2017 - 14:24

545

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Hensel lemma for schemes and henselian rings

Published on 04 Jul 2017 - 10:12

86

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How can I prove corollary 7.4 in Eisenbud's commutative algebra book?

Published on 27 Aug 2017 - 2:30

53

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Is $\gcd(2^m-1,2^n-1) = 2^{\gcd(m,n)}-1$ related to a Hensel lift?

Published on 10 Sep 2017 - 9:43

2.8k

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Hensel lifting square roots $\!\bmod p\,$ to $\!\bmod p^2$

Published on 24 Feb 2026 - 8:18

List Question

Using Hensel's Lemma to find the number of solutions.

$/6 = 10 \pmod {7^2}$

Finding primitive root of unity using Newton iteration

Coding Theory and Algebra

A $p$-adic unit is an $n^{th}$ power if it is congruent to a $n^{th}$ power mod $m$ (Eisenbud exercise)

Computing the quotient $\mathbb{Q}_p[x]/(x^2 + 1)$

square root of $-1$ in $\mathbb{Q}_p$

Squares in $\mathbb{Q}_p \bmod p$ (p-adic numbers)

$U/U_3 \equiv (\mathbb{Z}/27\mathbb{Z})^{\times}$

$\mathbb{Z}_p^*$ has a primitive $p - 1$-th root of unity (p-adic)

$\alpha \in \mathbb{Z}_p^{\times}$ iff there are infinitely many $n \in \mathbb{Z}_{>0}$ such that $X^n = \alpha$ has a solution.

Hensel lemma for schemes and henselian rings

How can I prove corollary 7.4 in Eisenbud's commutative algebra book?

Is $\gcd(2^m-1,2^n-1) = 2^{\gcd(m,n)}-1$ related to a Hensel lift?

Hensel lifting square roots $\!\bmod p\,$ to $\!\bmod p^2$

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