# Tagged Questions

Questions on problems that have yet to be completely solved by current mathematical methods.

1k views

### Result of solving an unsolved problem?

I was mulling over currently unsolved problems in mathematics (as I, and many others, find them quite interesting) and began to wonder what would happen if these problems were to be solved. I know ...
155 views

### Are there any perfect numbers which are also powerful?

Powerful numbers are discussed in this paper by R. A. Mollin and P. G. Walsh. Wikipedia has more information. In particular, note that OEIS A001694 does not seem to contain any (even) perfect ...
192 views

### Some contradiction in an open problem

Recently, I'm considerring an open problem from the paper by Ofelia T.Alas and others':On the extent of star countable spaces. It easily can be downloaded by google. The open Problem is this: ...
97 views

85 views

### Groups $\pi$ with $K(\pi, 1)$ a finite CW-complex

For what (say, finitely generated) groups $\pi$ is $K(\pi, 1)$ a finite CW-complex? Such a group must necessarily be torsion-free, since otherwise $H^*K(\pi, 1) = H^* \pi$ would be nontrivial in ...
122 views

### State of art of prime numbers distribution [closed]

I was reading some questions about prime numbers posted in latest days and a question came to my mind: What is the state of art of the research into prime numbers distribution? I read then ...
29 views

### Measure of convex hulls

I'm not an expert of this kind of questions, but I can't give a satisfactory answer to the following question. Pick $x_1\dots x_n \in \mathbb{R}^m$. Is there a formula for the measure of the ...
76 views

### Open problems in Galois theory (other than the IGP)

I'm interested in open problems in Galois theory. It's not necessary for them to be well known or considered important, but they have to be mostly Galois-theoretic, that is, not number theory or ...
57 views

### open problems regarding functions

I am looking for some open problems regarding functions. Problems like, Whether a function satisfying some properties say, X,Y,Z, exists or not, is unknown. Like there is no function $f(x)$ such ...
102 views

I'm very ignorant about results in number theory concerning the primes. Please let me know if these are open conjectures or easy problems: There are infinitely many primes of the form $n!+1$ There ...
145 views

### Coding Forcing Notions by Ordinal Numbers: A Possible Approach to Shelah-Foreman-Magidor Conjecture

Forcing notions are partial orders. In some sense each partial order is a "combination" of some well-orderings and each well-orderings is isomorphic to a unique ordinal number. Thus in some sense a ...
51 views

### Biggest Unsolved Problems In Graph Theory ( a la Riemann Hypothesis to Number Theory)

I'm not sure whether this is the right place for this question, but what are the most major unsolved problems in graph theory? (Not just a list, but something like a top 10 list or something like that)...
72 views

### Legendre's Conjecture Theme (Part I)

Main Question Recently I have been thinking about the Legendre's Conjecture. I noticed that a proof of the conjecture can be obtained if we can prove any one of the following, Conjecture 1. For ...
41 views

### Existence of a cycle of length $2^k$?

I was given a question which asks me to show that if each vertex of a graph has degree$\geq 3$, then it has a cycle whose length is some power of $2$. I have been able to show that it has a even ...
106 views

### Improving the bound $q < n\sqrt{3}$ for an odd perfect number $N = {q^k}{n^2}$ given in Eulerian form

(Note: This has been cross-posted to MO.) Let $N = {q^k}{n^2}$ be an odd perfect number given in Eulerian form (i.e., $q$ is prime with $q \equiv k \equiv 1 \pmod 4$ and $\gcd(q, n) = 1$). ...
154 views

### On the indivisibility of odd perfect numbers by small numbers

A good day to everyone! This question is an offshoot of the following MSE posts: Odd perfect number divisors Can an odd perfect number be divisible by $101$? My question is as follows: Is ...
83 views

### What do we know about Sorli's Conjecture and Odd Perfect Numbers?

I have seen that Jose Arnaldo Dris has recently published a great deal of literature concerning odd perfect numbers and Sorli's Conjecture. He claims that the truth of Sorli's conjecture implies that ...
88 views

### Apery's constant

I read that it is unknown if $\zeta (3)$ is algebraic but it is known to be irrational. Has anyone proved anything of the form $\zeta (3)$ is not a root of a polynomial of degree $12345$ with integer ...
111 views

### Are there infinitely many primes $p_k$ such that $(p_k-1)!+p_k$ is a also prime?

I am wondering whether there are infinitely many primes $p_k$ such that $(p_k-1)!+p_k$ is also prime. Given that $p_k \equiv 2 \pmod 3$. For a very large prime, I can assume Stirling's ...
258 views

### Open problems with practical outcome in a visible future?

[Note] The question has been asked at Matheoverflow. But there is no answers. I believe that any non-trivial idea will sooner or later find application in real life. However "sooner" is better than "...
433 views

### Would this proof strategy work for proving the lonely runner conjecture?

The problem is the lonely runner conjecture. This conjecture states that if $k$ runners begin running down a circle of unit circumference with random speeds, it will always the case that all runners ...
48 views

### Why is it called the *Inverse* Galois Problem?

This is just a very quick question and hopefully not poorly received. Question: Why is it called the inverse galois problem? The very brief statement given on wikipedia says Is every finite ...
334 views

### What is this variation of the traveling salesman problem called?

I've encountered a description of a well-known, hard to compute problem. Let us consider $n$ sites that need to be connected in the shortest possible way. If I am only allowed to connect the sites I ...
114 views

### How can I solve this problem without having to do it by hand?

I'm dealing with the following problem in computational programming. I'm trying to find a way to build an algorithm that can quickly resolve the following problem statement without forcing me to do it ...
106 views

### Is there any way to solve this problem without having to do it by hand? [duplicate]

I'm dealing with the following problem in computational programming. I'm trying to find a way to build an algorithm that can quickly resolve the following problem statement. Is there any way to group ...
246 views

### Collatz conjecture and related problems - mathematical machinery

Collatz conjecture stands as an open problem. That leads me to believe that the conjecture cannot be resolved by elementary means. Which brings me to my question: What techniques/machinery from ...
320 views

### Cube nets hexomino tilings.

I am looking for an ~12x12 rectangle (small holes and small obtrusions are okay) made entirely of cube net hexominos. It is my understanding that perfect rectangles, in general, are not possible ...
32 views

### Integers $n\geq 2$ such that there is an integer $k>1$ that divides both $n$ and $(n/k)+1$

I apologize to edit this question to request suggestions in this case for study on a sequence starting, $n\geq 2$ such that there is an integer $k>1$ that divides both $n$ and $(n/k)+1$, because it ...
68 views