List questions from p-adic-number-theory

Published on 18 Mar 2026 - 12:50

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Why introduce the $p$-adic numbers?

Published on 25 Mar 2026 - 15:24

86

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Forth Roots of $17$ in the P-adic Numbers

Published on 22 May 2017 - 16:54

535

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Integers are to natural numbers as $p$-adic integers are to what?

Published on 23 May 2017 - 22:10

51

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Expansion of $(1+X)^b$ when $b \in \mathbb{Z}_p$ and $b \notin \mathbb{N}$

Published on 25 May 2017 - 15:59

3.5k

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How to compute 2-adic square roots?

Published on 26 Mar 2026 - 12:42

1.3k

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Geometric series convergence in the p-adic numbers

Published on 28 May 2017 - 14:46

85

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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 25 Mar 2026 - 7:45

386

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What does the sequence $\{a^{p^n}\}$ converge to in $\mathbb{Q}_p$?

Published on 02 Jun 2017 - 3:20

1.6k

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On 5-adic representation of square root of -1

Published on 04 Jun 2017 - 21:54

140

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Harish-Chandra's submersive principle on closed subsets

Published on 27 Mar 2026 - 7:14

50

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Where can I learn more about varieties over the p-adic integers?

Published on 25 Mar 2026 - 20:10

162

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Problem with the ring of p-adic integers

Published on 07 Jun 2017 - 18:58

86

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Why are solutions $x=(x_1,\ldots,x_n)$ of a $p$-adic variety with one of the $x_i$ invertible called primitive solutions?

Published on 27 Mar 2026 - 23:35

92

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Why does invertibility of $2$ in $\mathbb{Z}_p$ guarantee that every element is a square?

Published on 10 Jun 2017 - 18:21

List Question

Limit of quotients by $p^n$-th powers in $p$-adic fields

Why introduce the $p$-adic numbers?

Forth Roots of $17$ in the P-adic Numbers

Integers are to natural numbers as $p$-adic integers are to what?

Expansion of $(1+X)^b$ when $b \in \mathbb{Z}_p$ and $b \notin \mathbb{N}$

How to compute 2-adic square roots?

Geometric series convergence in the p-adic numbers

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

What does the sequence $\{a^{p^n}\}$ converge to in $\mathbb{Q}_p$?

On 5-adic representation of square root of -1

Harish-Chandra's submersive principle on closed subsets

Where can I learn more about varieties over the p-adic integers?

Problem with the ring of p-adic integers

Why are solutions $x=(x_1,\ldots,x_n)$ of a $p$-adic variety with one of the $x_i$ invertible called primitive solutions?

Why does invertibility of $2$ in $\mathbb{Z}_p$ guarantee that every element is a square?

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