Question

Q is to prove that integer just above ($\sqrt{3} + 1)^{2n}$ is divisible by $2^{n+1}$ for all n belongs to natural numbers.

score 128 · Answer 1 · 2026-04-16 07:50:09

128

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Q is to prove that integer just above ($\sqrt{3} + 1)^{2n}$ is divisible by $2^{n+1}$ for all n belongs to natural numbers.

Published on 16 Apr 2026 - 7:50

score 48 · Answer 2 · 2026-04-14 00:40:24

48

Views

Issues proving ${n \choose s} \le (\frac{ne}{s})^s$ for $n,s \in N$

Published on 14 Apr 2026 - 0:40

score 91 · Answer 3 · 2026-04-10 23:18:44

91

Views

Is there constructivist proof for this measure theory fact?

Published on 10 Apr 2026 - 23:18

score 57 · Answer 4 · 2026-04-16 07:10:28

57

Views

Non-probabilistic proof for this infinite series identity related to the generalized negative binomial distribution?

Published on 16 Apr 2026 - 7:10

score 378 · Answer 5 · 2026-04-15 11:45:56

378

Views

Prove that $x\mapsto \mu(V+x)$ is lower semicontinuous (Big Rudin, Problem $2.23$)

Published on 15 Apr 2026 - 11:45

score 52 · Answer 6 · 2026-04-11 15:32:25

52

Views

Alternative proof by Induction

Published on 11 Apr 2026 - 15:32

score 549 · Answer 7 · 2026-04-10 17:46:02

549

Views

A measure $\mu$ on $(\mathbb{Z^+}, 2^{\mathbb{Z^+}})$ such that $\{\mu(E):E\subset\mathbb{Z^+}\}=[0,1]$

Published on 10 Apr 2026 - 17:46

score 555 · Answer 8 · 2026-04-14 17:36:25

555

Views

Let $A \in SO(3)$ show that $1$ is always an eigenvalue. (Proof check and alternative proof?)

Published on 14 Apr 2026 - 17:36

score 769 · Answer 9 · 2026-04-13 23:06:03

769

Views

If Sum of entries of all rows is equal then it is equal to one of the eigenvalue of the matrix.

Published on 13 Apr 2026 - 23:06

score 75 · Answer 10 · 2026-04-09 18:26:40

75

Views

Is right this proof, for limit of cosine as approaches 0 equal 1.

Published on 09 Apr 2026 - 18:26

score 65 · Answer 11 · 2026-04-16 12:29:49

65

Views

Given $ f: [a, b] \to \mathbb R $ and $ n \in \mathbb N $, assume $ h = \frac {b-a}{}\cdots$

Published on 16 Apr 2026 - 12:29

score 32 · Answer 12 · 2026-04-11 21:51:15

32

Views

Characterisation of Cartan algebra

Published on 11 Apr 2026 - 21:51

score 148 · Answer 13 · 2026-04-15 20:18:19

148

Views

Prove that $2a + 2ab + abc \leq 18$ when $a + b + c = 5$ where $a, b, c \in \mathbb{R}$ without calculus.

Published on 15 Apr 2026 - 20:18

score 889 · Answer 14 · 2026-04-17 18:53:33

889

Views

Dini's Theorem Proof on the Reals

Published on 17 Apr 2026 - 18:53

score 1.4k · Answer 15 · 2026-04-11 23:44:30

1.4k

Views

Novel (?) proof of the irrationality of $\sqrt3$

Published on 11 Apr 2026 - 23:44

List Question

Q is to prove that integer just above ($\sqrt{3} + 1)^{2n}$ is divisible by $2^{n+1}$ for all n belongs to natural numbers.

Issues proving ${n \choose s} \le (\frac{ne}{s})^s$ for $n,s \in N$

Is there constructivist proof for this measure theory fact?

Non-probabilistic proof for this infinite series identity related to the generalized negative binomial distribution?

Prove that $x\mapsto \mu(V+x)$ is lower semicontinuous (Big Rudin, Problem $2.23$)

Alternative proof by Induction

A measure $\mu$ on $(\mathbb{Z^+}, 2^{\mathbb{Z^+}})$ such that $\{\mu(E):E\subset\mathbb{Z^+}\}=[0,1]$

Let $A \in SO(3)$ show that $1$ is always an eigenvalue. (Proof check and alternative proof?)

If Sum of entries of all rows is equal then it is equal to one of the eigenvalue of the matrix.

Is right this proof, for limit of cosine as approaches 0 equal 1.

Given $ f: [a, b] \to \mathbb R $ and $ n \in \mathbb N $, assume $ h = \frac {b-a}{}\cdots$

Characterisation of Cartan algebra

Prove that $2a + 2ab + abc \leq 18$ when $a + b + c = 5$ where $a, b, c \in \mathbb{R}$ without calculus.

Dini's Theorem Proof on the Reals

Novel (?) proof of the irrationality of $\sqrt3$

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