Question

Prove that $2x^3+3x^2+x$ is always divisible by 6 if x is an integer.

score 1.7k · Answer 1 · 2026-04-15 03:18:38

1.7k

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Prove that $2x^3+3x^2+x$ is always divisible by 6 if x is an integer.

Published on 15 Apr 2026 - 3:18

score 1.2k · Answer 2 · 2026-04-11 02:27:36

1.2k

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How to prove that $n \sqrt{17}$ is irrational?

Published on 11 Apr 2026 - 2:27

score 246 · Answer 3 · 2026-04-14 16:12:36

246

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Proof verification: Null space of $A$ = $($Column space of $A^*)^\perp$ where $A\in M_{m\times n} (F)$

Published on 14 Apr 2026 - 16:12

score 32 · Answer 4 · 2026-04-16 16:58:19

Let A$\subset$B$\subset$C , and S a property. Can S implie c $\in$ B, and b $\in$ A given c,b satisfying S, and c$\in$C, b$\in$B?

score 111 · Answer 5 · 2026-04-14 11:00:02

111

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IS There a proof that if 4 points on a parabola have x coordinates summing to 0 then there is a circle that contains them all?

Published on 14 Apr 2026 - 11:00

score 60 · Answer 6 · 2026-04-13 16:58:02

60

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Prove that if $\Vert v+w \Vert^2 = \Vert v\Vert^2 + \Vert w\Vert^2$, then $v\cdot w = 0$

Published on 13 Apr 2026 - 16:58

score 696 · Answer 7 · 2026-04-15 02:53:09

696

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Proving that $0v = 0$ for any vector $v \in V$

Published on 15 Apr 2026 - 2:53

score 99 · Answer 8 · 2026-04-12 06:18:14

99

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Help me with an interesting number theory proof: Find all different [n/k] - floor function

Published on 12 Apr 2026 - 6:18

score 217 · Answer 9 · 2026-04-12 20:29:04

217

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Help me with this interesting and challenging to prove "fill the chessboard" problem

Published on 12 Apr 2026 - 20:29

score 530 · Answer 10 · 2026-04-15 19:46:43

530

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Proof of Shannon's entropy formula: Suppose that $p_1,...,p_n$, and $q_1,...,q_n$ are positive numbers...

Published on 15 Apr 2026 - 19:46

score 140 · Answer 11 · 2026-04-16 14:21:50

140

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Proof: Show that if _f_ and _g_ are monotone non-increasing real-valued functions on an open real interval...

Published on 16 Apr 2026 - 14:21

score 398 · Answer 12 · 2026-04-16 09:21:25

398

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Let $f:\mathbb{R}\rightarrow\mathbb{R}$ be differentiable. If there is an $L < 1$ such that for any $ x\in \mathbb{R}$ we have...

Published on 16 Apr 2026 - 9:21

score 227 · Answer 13 · 2026-04-13 21:46:44

227

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What is the justification in using logical equivalence to reformulate propositions?

Published on 13 Apr 2026 - 21:46

score 281 · Answer 14 · 2026-04-09 05:22:58

281

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Controlled natural language for mathematics

Published on 09 Apr 2026 - 5:22

score 7k · Answer 15 · 2026-04-12 02:05:33

7k

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Set Theory - Negation of the Union and Intersection operators

Published on 12 Apr 2026 - 2:05

List Question

Prove that $2x^3+3x^2+x$ is always divisible by 6 if x is an integer.

How to prove that $n \sqrt{17}$ is irrational?

Proof verification: Null space of $A$ = $($Column space of $A^*)^\perp$ where $A\in M_{m\times n} (F)$

Let A$\subset$B$\subset$C , and S a property. Can S implie c $\in$ B, and b $\in$ A given c,b satisfying S, and c$\in$C, b$\in$B?

IS There a proof that if 4 points on a parabola have x coordinates summing to 0 then there is a circle that contains them all?

Prove that if $\Vert v+w \Vert^2 = \Vert v\Vert^2 + \Vert w\Vert^2$, then $v\cdot w = 0$

Proving that $0v = 0$ for any vector $v \in V$

Help me with an interesting number theory proof: Find all different [n/k] - floor function

Help me with this interesting and challenging to prove "fill the chessboard" problem

Proof of Shannon's entropy formula: Suppose that $p_1,...,p_n$, and $q_1,...,q_n$ are positive numbers...

Proof: Show that if _f_ and _g_ are monotone non-increasing real-valued functions on an open real interval...

Let $f:\mathbb{R}\rightarrow\mathbb{R}$ be differentiable. If there is an $L < 1$ such that for any $ x\in \mathbb{R}$ we have...

What is the justification in using logical equivalence to reformulate propositions?

Controlled natural language for mathematics

Set Theory - Negation of the Union and Intersection operators

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