Questions tagged [conjectures]
for question related to conjectures.
204
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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 $A'$, $B'$,...
- 1,454
9
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1
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487
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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 $...
- 421
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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 ...
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0
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1
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111
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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\,, \...
- 1,454
13
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1
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466
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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 $a,b,c$...
- 2,997
4
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0
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144
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Is there a statement in Presburger arithmetic about primes this simple heuristic fails for?
I came up with the following conjecture while thinking about ways to formulate some heuristics about primes:
Conjecture: Given a statement $s$ in Presburger arithmetic, using an additional unary ...
- 3,064
1
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0
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151
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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 ...
- 1,305
3
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228
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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 ...
- 6,298
10
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561
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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 $\binom{n}{0},\binom{n}{1},\binom{n}{n-1},\binom{n}{n}$.
...
- 2,997
21
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1
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940
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Conjecture: Given any five points, we can always draw a pair of non-intersecting circles whose diameter endpoints are four of those points
The following question resisted attacks at Math SE, so I thought I would try posting it here.
Is the following conjecture true or false:
Given any five coplanar points, we can always draw at least ...
- 2,997
1
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0
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155
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Initial conditions to falsify Rowland's conjecture
Based on the Rowland's paper (A natural prime-generating recurrence), is there any theorem to show that for which initial condition $a(1) = k$ the conjecture can be falsified?
For example, for $k$ ...
- 151
6
votes
1
answer
349
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Different flavours of Vassiliev Conjecture
There is something that puzzles me about "Vassiliev's Conjecture". I am sure I am missing some detail which is obvious to the community, since there are several tightly related kind of ...
- 1,954
2
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111
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On a subset of the $abc$ triples
The $abc$ conjecture states that, for every positive real $\varepsilon$, there exist only finitely many triples $(a, b, c)$ of coprime positive integers such that $a + b = c$ and
$$c > \...
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0
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320
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How would one go about solving this conjecture concerning exponential Diophantine equations?
I’ve been working on the Collatz Conjecture, and I believe I’ve reduced it to a more tractable problem. Unless there are some errors I’ve overlooked, I have managed to reduce the Collatz Conjecture to ...
- 21
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Conjecture about primes and Fibonacci numbers
I posted this conjecture on math.stackexchange, but I received no answer proving or disproving it: if $ m > 4 $ is a positive integer not divisible by $ 2 $ or $ 3 $, it's ever possible to find a ...
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