Mathematics

Questions tagged [open-problem]

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

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Number of unordered factorizations of a non-square-free positive integer

I recently discovered that the number of multiplicative partitions of some integer $n$ with $i$ prime factors is given by the Bell number $B_i$, provided that $n$ is a square-free integer. So, is ...
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29 views

Set Cover Optimization of Cubes by Balls of Equal Radius

Let $C=[a,b]\subset R^n$ be a $n$-dimensional rectangle, $a,b\in R^n$. Find the minimal radius $r$ and set $x_1, \dotsc, x_N\in R^n$, for a given integer $N$ such that $$\bigcup_{i=1}^N B_r(x_i) \...
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2answers
84 views

What are the currently conjectures around symmetric group? [closed]

I am asking you this question: What are the currently conjectures around symmetric group on research? Indeed I am interested to work on unsolved problems concerning symmetric or alternating groups. ...
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41 views

Is it an open problem? (Sums of squares) [duplicate]

Has it been proven that if n can be represented as a sum of squares of two rational numbers, then it can also be represented as a sum of squares of two integers? This is a relatively simple statement, ...
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Open Problems in Homological Algebra

This time I want to ask about open problems in : 1.- Homological Algebra. 2.- Cohomology of Groups. 3.- Algebraic Topology. 4.- Galois Cohomology. Is there a list ? My motivation : I must to present a ...
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1answer
86 views

What is the true status of the Lehmer totient problem?

The Lehmer-totient problem : For a prime number $\ n\ $ we have $\ \varphi(n)=n-1\ $. In particular, we have $\ \varphi(n) \mid n-1\ $. Is there a composite number $\ n\ $ with $\ \varphi(n)\mid n-1\ ...
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1answer
34 views

Are there trigonometric and hyperbolic identities that are true in $\mathbb{R}$ but not true in $\mathbb{C}$

Question: Are there trigonometric and hyperbolic identities that are true in $\mathbb{R}$ but not true in $\mathbb{C}?$ For instance, $\cos^2(z)+\sin^2(z)=1$ is still true when we move to complex ...
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4answers
143 views

What is the closest mathematical area related to the Collatz Conjecture?

I want to study mathematics at university. But, it is extremely important that the area I have chosen is correct. I need to know this to deal with the Collatz Conjecture, which is famous in ...
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1answer
52 views

Current Open Problems Similar to the Basel Problem? [closed]

Are there any current open problems that are similar to the Basel problem?
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32 views

Open problems related to Euler's phi function

Carmichael's conjecture is a relatively known problem related to Euler's totient function. I just found out about Lehmer's totient problem which is another problem related to this function. I would ...
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0answers
57 views

Searching for unsolved problems in the field of stability

I have proposed an approach for constructing Lyapunov functions for autonomous systems in my Ph.D. thesis and find some useful examples. Now, I am searching for some another example in this field or ...
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38 views

Reference Request : The number of binary string with some special condition (open problem)

(Sorry for my poor english...) I wonder the reference of Simon Marais Mathematics competition 2019 problem B4. This problem is as follow. (They said this problem is open problem.) B4. A set $\...
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52 views

What is the current status of the snark theorem?

Wikipedia writes "W. T. Tutte conjectured that every snark has the Petersen graph as a minor... In 1999, Neil Robertson, Daniel P. Sanders, Paul Seymour, and Robin Thomas announced a proof of this ...
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30 views

Closed Nowhere dense is frentier of an open set

Excuse me can you see this question Every closed nowhere dense set is the frontier of an open set ... I tried on it but i am not sure , I prove it as follows Let $A$ is closed nowhere dense set, ...
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Interpretation and Implications of the Abundance Conjecture

So I'm interested in working on the Abundance conjecture, which states that for every projective variety $X$ with Kawamata log terminal singularities over a field $k$, if the canonical bundle $K_{X}$ ...
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1answer
49 views

Open Problems to do with Polynomials and/or Elementary Function Theory

I was wondering what are some open problems (even if deemed impossible) in basic function theory (stuff you'd learn in high school) and/or open problems to do with polynomials... Thank you in ...
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78 views

Should I waste my time with wolfram alpha to solve such problem like $x^3+y^3+z^3=390$?

I'm sorry to ask this question probably it is not suitable here. However I read some papers in number theory related to the solution of $x^3+y^3+z^3=n$ for some known solved problem about ...
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1answer
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Find all positive integers [closed]

Find all of non-null positive integers such that: $$(x-\frac{1}{yxz})\cdot (y-\frac{1}{yxz})\cdot (z-\frac{1}{xyz}) \in \mathbb{N}$$
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If $C_2$ is irrational, then there are infinitely many twin primes?

This is a natural follow-up after question 3629282. It is trivial that the irrationality of Brun's constant $B_2\approx1.90216$ implies that there are infinitely many twin primes: $$ B_2 \mbox{ is ...
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42 views

Status of Deligne's Weight-Monodromy Conjecture?

I'm interested in Deligne's weight-monodromy conjecture, and was wondering if anyone could provide any insight on its current status... What is completely resolved? What is being worked on and is ...
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24 views

Open questions in Probability

I was wondering if there are any really important or widely studied open problems in probability, we all know about the millennium problems list, but no one of those is directly related to probability....
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127 views

Proof that the twin prime constant is irrational (reference request)

It seems intuitively clear that the twin prime constant $$ C_2 = \prod_{p > 2} \left(1-\frac{1}{(p-1)^2} \right) \approx 0.66016 $$ is irrational. Can anyone please give a reference to a short ...
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list of open conjectures which are solved by students in high-Middle school level or receprocally?

I know only Snevily's conjecture which it was proved in 2009 by Bodan Arsovski. and He was a high-school student at the time., Are there other conjectures which are solved by students in high ...
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45 views

If $q^k n^2$ is an odd perfect number with special prime $q$, then $k \neq 1$ (MSE version)

Note that $\gcd(\sigma(q^k),\sigma(n^2))=i(q)=\gcd(n^2,\sigma(n^2))$ if and only if $\gcd(n,\sigma(n^2))=\gcd(n^2,\sigma(n^2))$. I have therefore undeleted this question, in view of this closely ...
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0answers
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Could be in mathematics an open problem solved by another open problem ?if yes any example?

In mathematics there are many open problems or open conjectures some of them had been solved and others are still open , it is good to know if there exist an example of open problem wich is solved by ...
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67 views

Open problems in Functions of One Complex Variable?

I am interested in complex variables, and only have knowledge for one variable, not several as of now... Regardless, I want to participate in some research... Do you guys know of any interesting open ...
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1answer
57 views

Chromatic number of plane and sphere [closed]

I've been studying Hadwiger–Nelson problem and several questions arose: 1) Is it easier to get an answer (chromatic number) for plane with different definition of distance? I mean, if we consider ...
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1answer
49 views

Possible relationship between non-divisors of odd perfect numbers and coefficients of corresponding cyclotomic polynomials?

A positive integer $n$ is called perfect if $\sigma(n)=2n$, where $$\sigma(n)=\sum_{d \mid n}{d}$$ is the sum of divisors of $n$. If $n$ is odd and $\sigma(n)=2n$, then $n$ is called an odd perfect ...
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1answer
38 views

What does Chowla's cosine problem actually ask to find?

The problem according to this description is: Let $ A \subseteq {\mathbb N} $ be a set of $ n $ positive integers and set $m(A) = - \min_x \sum_{a \in A} \cos(ax).$ What is $ m(n) = \min_A m(A) $? ...
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45 views

Research Topics in Operations Research

I'm a graduate student working on a course in which we are learning how to appropriately approach research in the mathematics field. I have been taking some courses over the last year on Operations ...
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0answers
52 views

Mathematical Consequences of $P=NP$ or $P\neq NP$ [closed]

It is common in mathematics to assume some unknown hypothesis or conjecture to be true or false, and then prove results dependent on said assumption. This can lead to many interesting developments ...
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1answer
280 views

Updated: Can someone have a look at a simple attempt towards a direct mathematical proof of the Collatz conjecture?

I am looking for feedback on the below, any is appreciated :) Remark: Apologies in advance for any incorrect use of notation as my mathematical experience is quite novice, additionally a word of ...
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1answer
40 views

Series sum of Fractional Fibonacci Series

Please help me proving that $\sum_{n=1}^{\infty} F(n)/(10^{-(n+1)}) = 0.011235955...$ Where F(n) are the Fibonacci Numbers
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3answers
106 views

Are there any sets where it is an open question whether the set is open (or closed)?

Proving whether a set is open or closed in a topological space can be difficult at times, so I'm curious if there are any sets where it is an open question whether they are open or closed. Obviously, ...
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0answers
170 views

Explicit results for the Collatz Conjecture? [closed]

I have some short questions I'd like to ask. I hope I'm asking in the right place. Has there been any significant progress on the Collatz Conjecture to date? What Tao really did was to set new ...
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3answers
87 views

Question with eight eight numbers [closed]

Suppose we have eight $8$ and we have to reach $1000$ with eight $8$. Use $+ \space - \space \times \space \div \space \sqrt{} \space \cdots $ to reach $1000$. Please help me to find at least one ...
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1answer
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What is unknown about the sphere $S^2$?

The standard sphere $S^2$ is (arguably) the simplest symmetrical geometric object. We can view $S^2$ as a smooth manifold in the category of smooth manifolds, or a Riemann sphere $\mathbb{P}^1$ in the ...
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44 views

Proof verification upper bound on the Mondrian Art Problem

I have been doing some thinking on the Mondrain Art Problem and think I may have discovered something. I think I have improved the upper bound for odd numbers from $k$ (for a $k$ by $k$ square) to $(...
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60 views

Given $n$, exist $k$ such that $2^k$ contains $n$ as string. [duplicate]

I have this doubt: Given $n\in \mathbb{N}$, does exist $k\in \mathbb{N}$ such that $2^k$ contains $n$ as a string in it? For example, $53$ is in $2^{16}=65\color{red}{53}6$. I just thought the ...
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Are there any odd perfect numbers in base $g$, where $g \neq 10$?

The topic of odd perfect numbers likely needs no introduction. Here is my primary question: Are there any odd perfect numbers in base $g$, where $g \neq 10$? Of course, there are several ...
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2answers
173 views

Do I understand the concept of $x^{0.84}$ correctly?

I'm trying to understand the concept of $x^{0.84}$ that Jeffrey Lagarias found for Collatz Conjecture. If I'm wrong, please correct me with an answer. I understand such that, Suppose the interval $\...
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3answers
301 views

Concept of undecidability and the Collatz problem [duplicate]

I'm reasoning like this: (I don't have enough math education) Suppose that the Collatz Conjecture is undecidable. This means, the Collatz conjecture cannot be proved to be true or false. This means, $...
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1answer
145 views

Is it officially proven that the Collatz sequences can't go to infinity?

Did the mathematician Jeffrey Lagarias prove that in his work the Collatz sequences could not go to infinity (divergent trajectory), that only cyclicity can exist? I don't have enough mathematics to ...
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3answers
277 views

Can anyone come up with an interesting consequence of the Twin Prime Conjecture being true?

The question is in the title. Was wondering if there are statements equivalent to or a consequence of the statement that there are infinitely many twin primes. If not, then why is this conjecture a "...
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3answers
155 views

Does the problem of P vs NP come under the category of Operational Research?

I am enrolled in Operational Research program. Also interested in Algorithms, I wish to know whether P vs NP is a common point in both of the fields, so that the effort put in understanding this ...
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2answers
4k views

What do mathematicians mean when they say some conjecture can’t be proven using the current technology?

When reading about some open problems, a lot of them have quotes by renowned mathematicians that “[the conjecture] cannot be solved using the current technology” or something along these lines. What ...
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0answers
260 views

Collatz conjecture, Tao-Collatz remainder and mod n.

Collatz conjecture is equivalent to $n\times 3^{k} = 2^{ak+1} - TCR$ where, for me, $k$=odd steps, and $ak+1 $=even steps. Note that total steps = k +( ak+1) steps. Some numbers have the same total ...
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2answers
318 views

Prove there is only one solution to the Diophantine equation $p^n - p = q^m - q$ where $p$ and $q$ are odd primes $p\gt q$

Consider numbers of the form $p^n - p$ where $p>2$ is a prime and $n>1 \in \mathbb{Z}$. How many of these have a unique representation? $2184$ can be written in this form $2$ ways, $3^7-3, 13^3-...
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2answers
98 views

Open conjecture in number theory without a good heuristic?

For most open conjectures in number theory , there are good heuristics that they are true : Examples include the Goldbach conjecture, the Collatz conjecture , the Riemann hypothesis and the twin prime ...
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1answer
154 views

"What is the specific mathematical reason behind the origin of the Collatz Conjecture that makes it difficult to solve it? [closed]

Is there a known so specific mathematical reason that makes it difficult to solve the Collatz Conjecture? Clearer: What is the specific mathematical reason behind the origin of the Collatz ...

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