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3
votes
1answer
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+500
Conjecture regarding trapping rational numbers in some special intervals
Conjecture:
Let $b\in\mathbb{N}_{\geq3}$ and $\{x_i\}$ be a collection of $b−2$ rational numbers greater than $1$. Does there always exist a natural number $a$ such that for all $i$ there exists some ...
6
votes
0answers
66 views
Examples of falsified (or currently open) longstanding conjectures leading to large bodies of incorrect results.
In general, the way that modern mathematical research is conducted isn't the way that many would assume is the ideal method of research. That is, mathematics is not the linear progression of ...
6
votes
0answers
69 views
Question regarding the status of Erdős' conjectures
Has Erdős' conjecture on arithmetic progressions or his conjecture on Sylvester's sequence been proven?
6
votes
0answers
155 views
Asymptotic FLT => FLT using ABC Conjecture
Edit:
I'm beginning to suspect I either misread the sources or perhaps something wasn't stated, but it's my guess now that there is no nontrivial way of showing the ABC conjecture implies Fermat's ...
3
votes
0answers
74 views
Prime clasfication by some constructive function
How to prove or justify the following:
$$ f(g)= \frac1{1-g^2} \prod_{k=1}^{\infty} \left(\frac{\sin(\pi \frac gk)}{\pi \frac gk} \cdot \frac 1{1-\frac{g^2}{k^2}}\right),
$$
The above statment can ...
2
votes
0answers
51 views
irreducibility conjecture
I tried to prove that every polynomial of the form
$f(m,n) := m\cdot x^{n-m}+(m+1)\cdot x^{n-m-1}+\cdots+(n-1)\cdot x+n \quad \text{with} \quad 0 < m < n$
is irreducible over the rationals for ...
1
vote
0answers
165 views
Can the openness of Gilbreath's conjecture be reduced to proof of the Riemann hypothesis?
As an information theoretician, it's a personal hobby of mine to find elegant analogies to open mathematical problems. After all, they have a profound impact on how I conduct my research and how I ...
0
votes
0answers
44 views
Which graphs satisfy this property?
I am currently looking into a conjecture in graph theory, known as the Jackson conjecture (1992). It says the following, in an equivalent formulation to its equivalent statement:
*Conjecture*Every ...
