# Questions tagged [conjectures]

For questions related to conjectures which are suspected to be true due to preliminary supporting evidence, but for which no proof or disproof has yet been found

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### Reference request for conjecture about bridge and crossing number of knots

Murasugi in his book (Knot theory and its applications, page 60) writes: Conjecture. If $K$ is a knot, then $c(K) \ge 3(br(K) - 1)$, where equality only holds when $K$ is the trivial knot, the ...
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### On the abundancy index of divisors of odd perfect numbers and a possible upper bound for the special/Euler prime

(Note: This post is an offshoot of this earlier question.) The topic of odd perfect numbers likely needs no introduction. Denote the sum of divisors of the positive integer $x$ by $\sigma(x)$, and ...
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### Does $k=1$ follow from $I(5^k)+I(m^2) \leq \frac{43}{15}$, if $p^k m^2$ is an odd perfect number with special prime $p=5$?

The topic of odd perfect numbers likely needs no introduction. Denote the sum of divisors of the positive integer $x$ by $\sigma(x)$, and denote the abundancy index of $x$ by $I(x)=\sigma(x)/x$. Euler ...
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Inspired by normal numbers I created the simple following problem: First take a rational number, for example $\frac{3}{4}$ which is equal to $0.75$; now add the first digit after the decimal separator ...
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### On Erdös-Szekeres convex polygons lower bound

I have problems with the construction of $2^{n-2}$ points that contain no n-gon, particulary, the proof of the book "Open Problems in Mathematics". The proof sais that: For $i = 0, ..., n-2$ ...
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### Is there an open mathematical conjecture which has been shown not to be provable in Peano Arithmetic before (possibly) being proved true?

There are several mathematical statements $\varphi$ about the natural numbers which are known to be true and known not to be provable in Peano Arithmetic (c.f. Gödel's incompleteness theorem, Paris-...
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### A conjectured upper bound for $\left(\frac{x^n+1}{x^{n-1}+1}\right)^n+\left(\frac{x+1}{2}\right)^n$ and $x\geq 1$

Hi I have (related https://mathoverflow.net/questions/337457/prove-that-left-fracxn1xn-11-rightn-left-fracx12-rightn ): Let $x\geq 1$ a real number and $n\geq 2$ a natural number then we have :...
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### To prove the existence of solution(s) of $\frac{a}{b+c}+\frac{b}{a+c}+\frac{c}{a+b}=4$

To prove if a certain equation has a solution, we do not need necessarily solve that equation. Example: Is there any point of the curve $y=\sin^2(x)/x$ between $x=0$ and $x=\pi$ so that the slope of ...
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### Is there any mathematical conjecture that is successfully applied in the real world in spite of being yet unproven? [closed]

I'm a philosophy student and I'm writing a thesis that makes a few comparisons between ethics and mathematics. My knowledge of mathematics is limited, however, and in the process of making my ...
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### Prove a conjecture, balls in boxes, n steps

My uncle gave me the following problem to work on (just for fun), he doesn't know whether the problem has a solution. I haven't been able to solve it and I give up, I don't think my current knowledge ...
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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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### A property implying union-closed sets conjecture condition

Given a union-closed family $\mathcal{F}$ of $n=\vert \mathcal{F} \vert$ sets, $n$ odd, and its family $\mathit{J}(\mathcal{F})$ of $m = \vert\mathit{J}(\mathcal{F})\vert$ basis sets (or $\cup$-...