# Questions tagged [open-problems]

If it turns out that a problem is equivalent to a known open problem, then the open-problem tag is added. After that, the question essentially becomes, "What is known about this problem? What are some possible ways to approach this problem? What are some ways that people have tried to attack it before, and with what results?"

**0**

**0**answers

### On improving the upper bound $I(m^2) \leq \frac{2p}{p+1}$, if $p^k m^2$ is an odd perfect number with special prime $p$ - Part II

**1**

**1**answer

### Polynomials, $3^x$ and the Collatz conjecture

**6**

**0**answers

### Is Collatz conjecture known to be true for specific numbers?

**1**

**3**answers

### On odd perfect numbers $p^k m^2$ with special prime $p$ satisfying $m^2 - p^k = 2^r t$ - Part II

**0**

**0**answers

### On improving the upper bound $I(m^2) \leq \frac{2p}{p+1}$, if $p^k m^2$ is an odd perfect number with special prime $p$

**13**

**2**answers

### Open problems in symbolic dynamics

**2**

**1**answer

### Planar subsets with many pairs of points on distance $1$

**2**

**0**answers

### Inscribed square and convexity

**4**

**0**answers

### Model theory and dynamical system (open problems)

**1**

**1**answer

### Simple example of Hammerstein integral equation

**3**

**1**answer

### Must Mersenne numbers be divisible by arbitrary large primes with exponent one?

**6**

**0**answers

### Is the unit-stick number of a knot equal to its stick number?

**24**

**0**answers

### 0's in 815915283247897734345611269596115894272000000000

**2**

**0**answers

### Factoring integers of the form $n=p q^2$ using elliptic curves

**1**

**1**answer

### Cramer–Castillon problem like

**11**

**1**answer

### Normal numbers, Liouville function, and the Riemann Hypothesis

**3**

**0**answers

### Dense sets in $\Bbb{R}^2$ with rational distance

**3**

**0**answers

### On RH in the Clay Institute list

**0**

**0**answers

### How small the radical of $xyz(x+y+z)$ can be infinitely?

**3**

**2**answers

### Open problems in matroid theory

**3**

**0**answers

### How to put a monetary incentive on an open research problem? [closed]

**7**

**2**answers

### Profound but not popular mathematical topics and notions

**2**

**0**answers

### Two more counterexamples to a conjecture from 1975 about hamiltonicity of digraphs

**5**

**2**answers

### Foundational results dependent on/equivalent to the continuum hypothesis or its negation?

**5**

**0**answers

### Frechet-Urysohn quotient of second countable locally compact Hausdorff space

**5**

**0**answers

### Heuristic for a density conjecture related to the Collatz $(3x+1)$-problem

**9**

**2**answers

### Generalized figures of constant width

**-2**

**2**answers

### Basic research problems references [closed]

**11**

**2**answers

### Which curves and surfaces are realizable by linkages? references?

**3**

**0**answers

### Effective radius of section of a convex set compared to that of the convex itself

**42**

**10**answers

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

**7**

**0**answers

### Isometries on the unit sphere

**0**

**1**answer

### Has Pillai conjecture been proven?

**6**

**2**answers

### Conjectures and open problems in representation theory [closed]

**34**

**1**answer

### Updates to Stanley's 1999 survey of positivity problems in algebraic combinatorics?

**7**

**0**answers

### When do two knots have isomorphic fundamental bikeis?

**13**

**2**answers

### Is every finite-order unimodular matrix conjugate to a $0,1,-1$ matrix?

**12**

**0**answers

### Is it an open problem whether fast-growing hierarchies can be defined without fundamental sequences?

**45**

**1**answer

### What's an example of an $\infty$-topos not equivalent to sheaves on a Grothendieck site?

**33**

**9**answers

### Decision problems for which it is unknown whether they are decidable

**8**

**1**answer

### A question regarding Kadison-Kaplansky idempotent conjecture (A nearest group element $g$ to a nontrivial self adjoint unitary element u )

**8**

**1**answer

### What is the state of research on finding all Prime Knots with 17 Crossings?

**13**

**1**answer

### Which knot invariants have no known diagram-independent descriptions?

**171**

**0**answers

### Why polynomials with coefficients $0,1$ like to have only factors with $0,1$ coefficients?

**1**

**1**answer

### The Total Graph is similar to a line graph

**2**

**0**answers

### How many solutions of x^3 +y^3 = z^3+3 are known? [duplicate]

**8**

**0**answers

### A cohomology associated to a (not necessarily integrable) distribution (Hilbert 16th problem and dynamical Lefschetz trace formula 2)

**7**

**1**answer

### Hyperbolic groups and spaces of negative curvature

**0**

**0**answers

### On the convergence of $\sum_{n\geq 1} \frac{\sin (2^n)}{n^s}$

**13**

**0**answers