List questions from p-adic-number-theory

Published on 24 Feb 2026 - 18:10

178

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Show that $\mathrm{SO}_3(\mathbb{Q}_p) \simeq \mathrm{SL}_2(\mathbb{Q}_p) $

Published on 06 Apr 2016 - 18:00

1.6k

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Majoration of the $p$-adic valuation of a factorial.

Published on 27 Mar 2026 - 14:55

149

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$p$-adic field with infinite residue field.

Published on 27 Mar 2026 - 14:45

152

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Please express the first 3 7-adic digits of a root of $x^3-1$ in $\mathbb{Z}_7$ other than 1.

Published on 13 Apr 2016 - 18:19

266

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P-adic expansions of Integers

Published on 14 Apr 2016 - 15:08

112

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If $a \in \mathbb{Z}_5$ and $a \equiv \pm1 \text{ }(\text{mod }5)$, does there exist $x \in \mathbb{Z}_5$ where $x^2 = a$?

Published on 15 Apr 2016 - 18:16

242

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Subgroups of finite index of the split maximal torus of $GL_n(\mathbb{Z}_p)$.

Published on 30 Mar 2026 - 0:05

245

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Rational sum of the $p$-adic series

Published on 18 Apr 2016 - 16:01

126

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Proving that $-1$ has no square root in $\mathbb Z_3$ (3-adic integers)

Published on 19 Apr 2016 - 2:05

358

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Limit of p-adic numbers

Published on 19 Apr 2016 - 19:06

304

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II. p-adic equations [2.1. Solutions] (J.-P. Serre)

Published on 25 Apr 2016 - 12:29

169

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Proving that $\mathbb{Q}_p$ is not formally real.

Published on 27 Mar 2026 - 14:45

306

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Changing uniformizer of $p$-adics

Published on 26 Apr 2016 - 18:38

544

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A question about the definition of $p$-adic pseudo-measure.

Published on 27 Apr 2016 - 19:39

List Question

Can the zeroes of a multivariate $p$-adic polynomial be bounded?

Show that $\mathrm{SO}_3(\mathbb{Q}_p) \simeq \mathrm{SL}_2(\mathbb{Q}_p) $

Majoration of the $p$-adic valuation of a factorial.

$p$-adic field with infinite residue field.

Please express the first 3 7-adic digits of a root of $x^3-1$ in $\mathbb{Z}_7$ other than 1.

P-adic expansions of Integers

If $a \in \mathbb{Z}_5$ and $a \equiv \pm1 \text{ }(\text{mod }5)$, does there exist $x \in \mathbb{Z}_5$ where $x^2 = a$?

Subgroups of finite index of the split maximal torus of $GL_n(\mathbb{Z}_p)$.

Rational sum of the $p$-adic series

Proving that $-1$ has no square root in $\mathbb Z_3$ (3-adic integers)

Limit of p-adic numbers

II. p-adic equations [2.1. Solutions] (J.-P. Serre)

Proving that $\mathbb{Q}_p$ is not formally real.

Changing uniformizer of $p$-adics

A question about the definition of $p$-adic pseudo-measure.

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