Questions tagged [conjectures]
for question related to conjectures.
15 questions from the last 365 days
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Conjecture about Euler quotients related to non-Wieferich numbers $W(n)=\frac{2^n+1}{3}$
For odd natural $n$ define the Euler quotient:
$$ a(n)=\frac{(2^{\phi(n)}-1) \bmod n^2}{n}=\frac{2^{\phi(n)}-1}{n} \bmod n$$
$a(n)=0$ is $n$ being Wieferich number (not necessarily prime).
For odd $n$,...
- 25.4k
2
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76
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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 ...
1
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0
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152
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A new Conjecture at OEIS sequence A376842
Here is a new conjecture of mine from the appendix of an unpublished manuscript currently under review.
Let $b \in \mathbb{Z}^+$ and assume that $n$ is an integer greater than $1$ and not a multiple ...
- 1,451
3
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193
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Are local complete intersections of small codimension necessarily (global) complete intersections?
Hartshorne's 1974 conjecture states that a smooth closed subvariety $X$ of $\mathbb{CP}^r$ of dimension $>2/3r$ is necessarily (globally) a complete intersection. Is anything interesting known ...
- 16.9k
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241
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Conjecture about some recurrent primes
I want to know if there are conjectures similar to this one, I know there is the Bell primes conjecture or Gardner conjecture (mentioned in this page https://en.wikipedia.org/wiki/Bell_number), but ...
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374
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Is the Conjecture of Representing Integers as Differences of Semiprimes and Primes Extendable to Products of Distinct Primes?
Conjecture:
Let $k$ and $l$ be fixed distinct positive integers ($k≠l$). Then, for every positive integer $n$, there exist prime numbers $p_1,p_2,…,p_k∈\mathbb{P}$ and $q_1,q_2,…,q_l∈\mathbb{P}$ such ...
- 17
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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
5
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1
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811
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A consequence of Firoozbakht's conjecture?
This is a question out of curiosity, while looking at the Firoozbakht's conjecture. It might not be research related, but as usual, I am not really sure if a question ever is research related or not, ...
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3
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A generalization of Barrow's inequality
More than seven years ago. I posted this problem in stackexchange:
Let $ABC$ be a triangle, $P$ be arbitrary point inside of $ABC$. Let $A_1B_1C_1$ be the tangential traingle of $ABC$. Let $A'$, $B'$,...
- 1,776
9
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1
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553
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Does the sequence formed by Intersecting angle bisector in a pentagon converge?
I asked this question on MSE here.
Given a non-regular pentagon $A_1B_1C_1D_1E_1$ with no two adjacent angle having a sum of 360 degrees, from the pentagon $A_nB_nC_nD_nE_n$ construct the pentagon $...
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1
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229
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Can the Collatz conjecture be independent of ZFC? [closed]
It is known that the Continuum Hypothesis is independent of ZFC.
The formulation of the Collatz conjecture looks somehow more simple than that of the Continuum Hypothesis.
Is it possible that the ...
- 654
0
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1
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140
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Rearrangement inequality for sum
Rearrangement inequality:
Assume we have finite ordered sequences of nonnegative real numbers $0 \le a_1 \le a_2 \le\cdots\le a_n \quad\text{and}\quad 0\le b_1 \le b_2 \le\cdots\le b_n, \cdots\,, \...
- 1,776
13
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1
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484
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A probability involving areas in a random pentagram inscribed in a circle: Is it really just $\frac12$?
This question was posted at MSE but was not answered.
The vertices of a pentagram are five uniformly random points on a circle. The areas of three consecutive triangular "petals" are $a,b,c$...
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Optimal covering trails for every $k$-dimensional cubic lattice $\mathbb{N}^k := \{(x_1, x_2, \dots, x_n) : x_i \in \mathbb{N} \wedge n \geq 3\}$
After a dozen years spent investigating this particular class of problems, I finally give up and I wish to ask you if any improvement is achievable from here on.
The general problem is as follows:
Let ...
- 1,451
3
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234
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Uses of excluded middle on a conjecture that can be rewritten constructively with this trick
An interesting proof technique is to use the law of excluded middle on a conjecture. There are proofs using LEM on the Riemann hypothesis for example.
Constructively this is disallowed (if you can ...
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