All Questions
Tagged with conjectures reference-request
29 questions
2
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Does a matrix ring over a ring satisfy the Koethe conjecture if the coefficient ring itself satisfies the Koethe conjecture?
I just want to know whether the following statement is true or false.
If $R$ is a ring satisfying the Koethe conjecture, then the matrix ring over $R$ also satisfies the Koethe conjecture.
Or is it ...
0
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1
answer
150
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Inequality $(a_1^x+a_2^x+\cdots+a_n^x)^y \ge (a_1^y+a_2^y+\cdots+a_n^y)^x$
Conjecture: Let $a_1, a_2, \cdots , a_n>0$ and $y \ge x $ then
$$(a_1^x+a_2^x+\cdots+a_n^x)^y \ge (a_1^y+a_2^y+\cdots+a_n^y)^x$$
Equality iff $x=y$
Is the conjecture right? Have you ever seen this ...
- 1,776
10
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0
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598
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Does the interior of Pascal's triangle contain three consecutive integers?
This question defeated Math SE, so I am posting it here.
Consider the interior of Pascal's triangle: the triangle without numbers of the form $\binom{n}{0},\binom{n}{1},\binom{n}{n-1},\binom{n}{n}$.
...
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11
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3
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711
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An open triangle problem in plane geometry
Some years ago, I asked some 'famous' people in an advanced Plane Geometry forum about the following:
Let $ABC$ be arbitrary triangle, how can one construct a point $P$ in the plane such that $P$ is ...
- 1,776
8
votes
1
answer
888
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Statement of classical Ramanujan-Petersson conjecture
I'm preparing for an expository talk on some topics in the representation theory of reductive p-adic groups, including tempered representations and Whittaker models, and as motivation I wanted to ...
- 815
9
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1
answer
505
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Status of a conjecture of Hirzebruch
I was reading a paper from 1994 which claimed that the following statement was a conjecture of Hirzerbruch:
If a complex surface X is homeomorphic to either $S^2 \times S^2$ or $\mathbb{C}P^2 \# \...
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9
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1
answer
388
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$π(x+y) - π(x) ≤ c·y/\ln(y)$ for some constant $c$?
(I posted this question on Math SE but it has had no answer for a year now so I would like to ask if anyone here can provide one.)
Thinking about the prime number theorem, I wondered whether it is ...
- 2,912
5
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2
answers
391
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Conjecture about minimal number of edge crossings in complete bipartite graphs
I am interested in the status of the conjecture about the minimum number of edge crossings $cr(K_{m,n})$ in a drawing of the complete bipartite graph $K_{m,n}$.
The Wikipedia article https://en....
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8
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0
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346
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A generalization of Feit–Thompson conjecture, for square-free integers
I asked the following question with my account that I have for these sites Mathematics Stack Exchange and MathOverflow. The bounty that I offered in MSE expired without answers. The post that I refer ...
6
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2
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1k
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Conjectures and open problems in representation theory [closed]
Are there very famous open problems or conjectures in representation theory, or in enumerative geometry, like the volume conjecture in topology?
-2
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1
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396
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Published articles in journals about the Firoozbakht's conjecture, whose main goal or focus is the study of this conjecture
I would like to know what articles are in the literature about the known as Firoozbakht's conjecture, see the Wikipedia Firoozbakht's conjecture.
Question. What articles have been published in ...
-2
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1
answer
260
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Is the conjecture $min(A,B) \le rad(ABC)$ new and correct? [closed]
$\DeclareMathOperator\rad{rad}$Conjecture: If $A, B, C$ are positive integers with $\gcd(A, B)=1$, $\gcd(B, C)=1$, and $\gcd(C, A)=1$, and if $A+B=C$, then $\min(A,B) \le \rad(ABC)$.
If the ...
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5
votes
5
answers
274
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Peculiarities in low dimensions or low order or etc
I have been pondering about certain conjectures and theorems viewed as either low vs high dimensions, or smaller vs larger primes, or anything of the sort "low vs high order". Let me mention a couple ...
2
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0
answers
278
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Asymptotics of Littlewood polynomials
Littlewood in [L] states several conjectures regarding asymptotics of polynomials with $\pm1$ coefficients.
He considers the class $\mathscr F$ of polynomials of form $\sum^n\pm z^m$ and asks whether ...
- 1,583
5
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1
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472
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Is the following weak version of second Hardy-Littlewood conjecture already known?
Very recently I was going through my previous MSE posts and I stumbled upon some of them regarding the Second Hardy-Littlewood Conjecture which states that,
For all $x,y\ge 2$ we have, $$\pi(x)+\...
user57432
3
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3
answers
348
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A rearrangement inequality for exponentiation function
Update: A year ago, but the first answer is not clear with me. I bounty this question again.
My question: I am looking for a proof or counterexample to the following inequality:
If $n \in \mathbb{...
- 1,776
8
votes
1
answer
449
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Does Vizing's conjecture hold for the infinite graphs?
In finite graph theory, there are many (in)equalities which relate the integer value of a certain graph invariant (e.g. domination or chromatic number) for the product of two finite graphs (e.g. ...
12
votes
2
answers
556
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Sylvester–Gallai theorem with circle version, plane version and curve version?
The Sylvester–Gallai theorem in geometry states that, given a finite number of points in the Euclidean plane, either
All the points are collinear; or
There is a line which contains exactly two of the ...
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18
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1
answer
1k
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Which motivic cohomology groups of complex numbers are non-torsion?
I would like to know which motivic cohomology groups of complex numbers are non-zero and ("better") non-torsion, i.e., for which $(i,j)$ the $i$th cohomology of the complex ${\mathbb{Q}}(j)$ over $\...
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1
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0
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142
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Primes dividing functions defined by linear recurrence relations with constant coefficients
For Fibonacci numbers $F_n$ it holds that $p|F_{p-(\frac{5}{p})}$, if $p$ is an odd prime (Legendre symbol).
I guessed that the number $5$ came from the roots of the characteristic polynomial and ...
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26
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1
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1k
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What is the status on this conjecture on arithmetic progressions of primes?
The Green-Tao theorem states that for every $n$, there is an arithmetic sequence of length $n$ consisting of primes.
For primes, $p$, let $P(p)$ be the maximum length of an arithmetic progression of ...
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3
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0
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177
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Looking for an appropriate reference(s) for two conjectures on odd perfect numbers
(I apologize in advance if this question is unsuitable for MO. If so, please let me know and I will migrate it to MSE.)
Let $\sigma(M)$ be the sum of the divisors of the positive integer $M$. For ...
10
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0
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405
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A conjecture of Blakley and Dixon about odd powers of positive matrices
In a 1966 paper Blakley and Dixon conjecture the following. Let $S$ be a symmetric matrix with nonnegative entries and let $u$ be a unit vector with nonnegative entries. For integers $k\ge j$ both odd,...
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7
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0
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253
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What is the status of this fifty-year-old conjecture of Kostant?
On page 3.27 of his 1963 thesis on the cohomology of homogeneous spaces as approached through the Eilenberg–Moore spectral sequence, Paul Baum states the following conjecture, which he attributes to B....
- 2,995
5
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0
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425
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Conjectured new primality test for Mersenne numbers
How to prove that this conjecture about a new primality test for Mersenne numbers is true ?
Definition: Let $M_{q}=2^{q}-1 , S_{0} = 3^{2} + 1/3^{2} , \ and: \ S_{i+1} = S_{i}^{2}-2 \pmod{M_{q}}$
...
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7
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What will be the consequences if second Hardy-Littlewood conjecture turns out to be true?
It is generally believed that the Second Hardy-Littlewood Conjecture is false. But it has not been proved (or disproved) yet. My question is,
What would be the consequences if Second Hardy-Littlewood ...
user57432
4
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0
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748
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Second Hardy-Littlewood Conjecture theme
If Second Hardy-Littlewood Conjecture is true then we can claim that $\pi(x)-\pi(y)\leq \pi(x-y)$. Thus the conjecture gives an upper bound for the number of primes between $x$ and $y$. I have found ...
user57432
5
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1
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604
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Who is attributed with the conjecture that every multiply-perfect number greater than $1$ is even?
I know that Descartes is considered to be the first to ask whether or not odd perfect numbers exist ($n$ such that $\sigma(n)=2n$, where $\sigma(n)$ is the sum of divisors of $n$), and he also ...
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15
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1
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Status of Grothendieck's conjecture on homomorphisms of abelian schemes
In [1] Grothendieck posits the following:
Conjecture. Let $S$ be a reduced connected scheme, locally of finite type over Spec($\mathbf{Z}$) or a field $k$, $A$ and $B$ two abelian schemes over $S$, $...
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