Question

Prove that for every natural number $a$ there are integers $t \geq 0$ and $r$ such that $a = 3^t r$ and 3 does not divide r.

score 72 · Answer 1 · 2026-03-25 23:42:20

72

Views

Prove that for every natural number $a$ there are integers $t \geq 0$ and $r$ such that $a = 3^t r$ and 3 does not divide r.

Published on 25 Mar 2026 - 23:42

score 242 · Answer 2 · 2026-03-29 13:40:25

242

Views

overdetermined system of non-linear equations

Published on 29 Mar 2026 - 13:40

score 34 · Answer 3 · 2026-03-31 21:13:36

34

Views

Formally deriving a vacuous truth from a definition involving conjoined implications

Published on 31 Mar 2026 - 21:13

score 634 · Answer 4 · 2019-04-21 01:48:53

634

Views

General Point set Topology: The Closure of a set is Closed

Published on 21 Apr 2019 - 1:48

score 131 · Answer 5 · 2019-04-21 18:03:27

131

Views

Theorem 24.3 in Munkres's Topology

Published on 21 Apr 2019 - 18:03

score 3.5k · Answer 6 · 2026-03-25 11:23:38

3.5k

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Using the Cauchy-Riemann Equations, prove that $\operatorname{Log}(z)$ is holomorphic in $\mathbb{C}\setminus[0,\infty)$ and explain why

Published on 25 Mar 2026 - 11:23

score 81 · Answer 7 · 2026-03-25 11:10:14

81

Views

Understanding Proof about Continued Fraction convergent sequences

Published on 25 Mar 2026 - 11:10

score 166 · Answer 8 · 2019-04-22 21:36:07

166

Views

Why if $0 <|\lambda| < 1,$ then $(U^{-1} - \frac{1}{\lambda}I)$ invertible?

Published on 22 Apr 2019 - 21:36

score 303 · Answer 9 · 2026-03-30 08:17:47

303

Views

If $x_n \rightarrow x \implies \lim_{n \rightarrow +\infty}$ $f_n (x_n) \rightarrow f(x)$ ,then $f_n \rightarrow f$ uniformly in each compact set $K $

Published on 30 Mar 2026 - 8:17

score 348 · Answer 10 · 2019-04-23 13:59:42

348

Views

Integral test with $f$ negative and increasing?

Published on 23 Apr 2019 - 13:59

score 69 · Answer 11 · 2026-03-25 06:01:29

69

Views

Proving the Poisson differential is a coboundary map

Published on 25 Mar 2026 - 6:01

score 443 · Answer 12 · 2026-04-06 20:21:10

443

Views

Explanation for Oxtoby's proof: a nonempty topological space $X$ is Baire iff player (I) has no winning strategy in the Choquet game

Published on 06 Apr 2026 - 20:21

score 104 · Answer 13 · 2026-03-29 16:49:26

104

Views

Why can we apply Fubini's theorem here?

Published on 29 Mar 2026 - 16:49

score 49 · Answer 14 · 2026-04-02 07:30:20

49

Views

Why a particular module over a DVR is cyclic if it's quotient and kernel are cyclic?

Published on 02 Apr 2026 - 7:30

score 56 · Answer 15 · 2026-02-23 04:17:47

56

Views

How does $(\mathfrak {B_2} / \mathfrak {B_1}) \cap (R/ \mathfrak p) = (0)$?

Published on 23 Feb 2026 - 4:17

List Question

Prove that for every natural number $a$ there are integers $t \geq 0$ and $r$ such that $a = 3^t r$ and 3 does not divide r.

overdetermined system of non-linear equations

Formally deriving a vacuous truth from a definition involving conjoined implications

General Point set Topology: The Closure of a set is Closed

Theorem 24.3 in Munkres's Topology

Using the Cauchy-Riemann Equations, prove that $\operatorname{Log}(z)$ is holomorphic in $\mathbb{C}\setminus[0,\infty)$ and explain why

Understanding Proof about Continued Fraction convergent sequences

Why if $0 <|\lambda| < 1,$ then $(U^{-1} - \frac{1}{\lambda}I)$ invertible?

If $x_n \rightarrow x \implies \lim_{n \rightarrow +\infty}$ $f_n (x_n) \rightarrow f(x)$ ,then $f_n \rightarrow f$ uniformly in each compact set $K $

Integral test with $f$ negative and increasing?

Proving the Poisson differential is a coboundary map

Explanation for Oxtoby's proof: a nonempty topological space $X$ is Baire iff player (I) has no winning strategy in the Choquet game

Why can we apply Fubini's theorem here?

Why a particular module over a DVR is cyclic if it's quotient and kernel are cyclic?

How does $(\mathfrak {B_2} / \mathfrak {B_1}) \cap (R/ \mathfrak p) = (0)$?

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