Question

Prove that if $2n+1$ and $3n+1$ are both perfect squares then $40|n$.

score 1.8k · Answer 1 · 2016-05-07 15:49:19

1.8k

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Prove that if $2n+1$ and $3n+1$ are both perfect squares then $40|n$.

Published on 07 May 2016 - 15:49

score 326 · Answer 2 · 2026-04-08 19:27:38

326

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Proof verification : a very useful theorem (in measure theory)

Published on 08 Apr 2026 - 19:27

score 2.2k · Answer 3 · 2016-05-08 04:22:14

2.2k

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Constructing a square from the difference of diagonal and side

Published on 08 May 2016 - 4:22

score 144 · Answer 4 · 2026-04-05 02:37:30

144

Views

Sum of cardinals of all intersections: elegant alternative proofs?

Published on 05 Apr 2026 - 2:37

score 663 · Answer 5 · 2016-05-09 03:16:07

663

Views

There exists polynomial $(P_{n})_{n\in\mathbb{N}}$ such that $P_n(0)=1$, and $\lim_{n\rightarrow \infty}P_{n}(z)=0$..

Published on 09 May 2016 - 3:16

score 74 · Answer 6 · 2016-05-10 03:34:52

74

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Show $P(\frac{1}{n}\sum_{i=1}^{n}Y_i\geq c)\leq e^{-nd}$ for constants $c$ and $d$

Published on 10 May 2016 - 3:34

score 73 · Answer 7 · 2016-05-10 04:54:24

73

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Request for a proof that $\sum\limits_{i=1}^n i^{k+1}=(n+1)\sum\limits_{i=1}^n i^k-\sum\limits_{p=1}^n\sum\limits_{i=1}^p i^k$

Published on 10 May 2016 - 4:54

score 100 · Answer 8 · 2016-05-14 09:20:04

100

Views

Prove that $\int _e^\infty \frac{\ln(x)}{x^p} dx$ is divergent for $p \le1$.

Published on 14 May 2016 - 9:20

score 1.6k · Answer 9 · 2026-03-28 10:15:57

1.6k

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Subfield of $\mathbb{Q}(\sqrt[n]{a})$

Published on 28 Mar 2026 - 10:15

score 70 · Answer 10 · 2016-05-17 05:29:32

70

Views

Not sure how to prove this statement by contradiction?

Published on 17 May 2016 - 5:29

score 731 · Answer 11 · 2016-05-17 09:50:11

731

Views

Convergence of the power of a matrix : a simpler proof?

Published on 17 May 2016 - 9:50

score 760 · Answer 12 · 2016-05-18 10:18:37

760

Views

Alternative proof of Euler's result that $641$ divides $2^{32} + 1$

Published on 18 May 2016 - 10:18

score 39 · Answer 13 · 2026-04-07 16:20:27

39

Views

What is a useful starting idea to think about this simple graph problem?

Published on 07 Apr 2026 - 16:20

score 78 · Answer 14 · 2016-05-19 12:31:20

78

Views

How to fill in the gaps in my proof to make it more convincing?

Published on 19 May 2016 - 12:31

score 1.2k · Answer 15 · 2026-04-04 07:53:39

1.2k

Views

Alternative proof of Fundamental Lemma of Variational Calculus?

Published on 04 Apr 2026 - 7:53

List Question

Prove that if $2n+1$ and $3n+1$ are both perfect squares then $40|n$.

Proof verification : a very useful theorem (in measure theory)

Constructing a square from the difference of diagonal and side

Sum of cardinals of all intersections: elegant alternative proofs?

There exists polynomial $(P_{n})_{n\in\mathbb{N}}$ such that $P_n(0)=1$, and $\lim_{n\rightarrow \infty}P_{n}(z)=0$..

Show $P(\frac{1}{n}\sum_{i=1}^{n}Y_i\geq c)\leq e^{-nd}$ for constants $c$ and $d$

Request for a proof that $\sum\limits_{i=1}^n i^{k+1}=(n+1)\sum\limits_{i=1}^n i^k-\sum\limits_{p=1}^n\sum\limits_{i=1}^p i^k$

Prove that $\int _e^\infty \frac{\ln(x)}{x^p} dx$ is divergent for $p \le1$.

Subfield of $\mathbb{Q}(\sqrt[n]{a})$

Not sure how to prove this statement by contradiction?

Convergence of the power of a matrix : a simpler proof?

Alternative proof of Euler's result that $641$ divides $2^{32} + 1$

What is a useful starting idea to think about this simple graph problem?

How to fill in the gaps in my proof to make it more convincing?

Alternative proof of Fundamental Lemma of Variational Calculus?

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