# Linked Questions

38 questions linked to/from Not especially famous, long-open problems which anyone can understand

**33**

votes

**62**answers

19k views

### What's your favorite equation, formula, identity or inequality? [closed]

Certain formulas I really enjoy looking at like the Euler-Maclaurin formula or the Leibniz integral rule. What's your favorite equation, formula, identity or inequality?

**62**

votes

**28**answers

10k views

### Examples of seemingly elementary problems that are hard to solve?

I'm looking for a list of problems such that
a) any undergraduate student who took multivariable calculus and linear algebra can understand the statements, (Edit: the definition of understanding here ...

**52**

votes

**14**answers

15k views

### Open problems in Euclidean geometry?

What are some (research level) open problems in Euclidean geometry ?
(Edit: I ask just out of curiosity, to understand how -and if- nowadays this is not a "dead" field yet)
I should clarify a bit ...

**84**

votes

**4**answers

12k views

### Is the series $\sum_n|\sin n|^n/n$ convergent?

Problem. Is the series $$\sum_{n=1}^\infty\frac{|\sin(n)|^n}n$$convergent?
(The problem was posed on 22.06.2017 by Ph D students of H.Steinhaus Center of Wroclaw Polytechnica. The promised prize for ...

**151**

votes

**3**answers

27k views

### Convergence of $\sum(n^3\sin^2n)^{-1}$

I saw a while ago in a book by Clifford Pickover, that whether $\displaystyle \sum_{n=1}^\infty\frac1{n^3\sin^2 n}$ converges is open.
I would think that the question of its convergence is really ...

**88**

votes

**5**answers

8k views

### Is there a dense subset of the real plane with all pairwise distances rational?

I heard the following two questions recently from Carl Mummert, who encouraged me to spread them around. Part of his motivation for the questions was to give the subject of computable model theory ...

**75**

votes

**6**answers

12k views

### Can we cover the unit square by these rectangles?

The following question was a research exercise (i.e. an open problem) in R. Graham, D.E. Knuth, and O. Patashnik, "Concrete Mathematics", 1988, chapter 1.
It is easy to show that
$$\sum_{1 \...

**42**

votes

**10**answers

4k views

### List of long open, elementary problems which are computational in nature

I would like to ask a question of a similar vein to this question.
Question: I'm asking for a list of long open problems which are computational in nature which a beginning graduate student can ...

**52**

votes

**8**answers

5k views

### Two (probably) equal real numbers which are not proved to be equal?

Can someone give me a nice example of two computable real numbers which are believed but not proved to be equal?
I never really understood the assertion that "the reals do not have decidable equality"...

**54**

votes

**7**answers

6k views

### Status of PL topology

I posted this question on math stackexchange but received no answers. Since I know there are more people knowledgeable in geometric and piecewise-linear (PL) topology here, I'm reposting the question. ...

**40**

votes

**12**answers

2k views

### Can a discrete set of the plane of uniform density intersect all large triangles?

Let S be a discrete subset of the Euclidean plane such that the number of points in a large disc is approximately equal to the area of the disc. Does the complement of S necessarily contain triangles ...

**61**

votes

**4**answers

4k views

### What is the limit of gcd(1! + 2! + … + (n-1)! , n!) ?

Let $s_n = \sum_{i=1}^{n-1} i!$ and let $g_n = \gcd (s_n, n!)$. Then it is easy to see that $g_n$ divides $g_{n+1}$. The first few values of $g_n$, starting at $n=2$ are $1, 3, 3, 3, 9, 9, 9, 9, 9, ...

**16**

votes

**10**answers

5k views

### Not especially famous, long-open problems which higher mathematics beginners can understand

This is a pair to
Not especially famous, long-open problems which anyone can understand
So this time I'm asking for open questions so easy to state for students of subjects such as undergraduate ...

**25**

votes

**6**answers

1k views

### For which $n$ is there a permutation such that the sum of any two adjacent elements is a prime?

For which $n$ is it possible to find a permutation of the numbers from $1$ to $n$ such that the sum of any two adjacent elements of the permutation is a prime?
For example: For $n=4$ the permutation $...

**22**

votes

**4**answers

1k views

### Freeness of a Z[x]-module

Definition: Call a mapping $f: \mathbb{Z} \rightarrow \mathbb{Z}$
a generalized polynomial if for any distinct integers $m$ and $n$
we have $(m - n)|(f(m)-f(n))$.
It is easy to check that polynomial ...