# Tagged Questions

for question related to conjectures.

24 views

### If $N = q^k n^2$ is an odd perfect number, if $n < q^{k+1}$, does it follow that $k > 1$?

Let $N = q^k n^2$ be an odd perfect number with Euler prime $q$. According to Dickson (as pointed out recently by Beasley), Descartes conjectured $k=1$ in a letter to Mersenne in 1638, with Frenicle'...
99 views

140 views

### What explains the asymptotic and the pattern in this sequence related to Riemann zeta zeros?

As the starting point for my experiment I assumed that the imaginary parts of the Riemann zeta zeros are of the form: $$\Im \{ \rho_n \} = \frac{2\pi}{\log x_n}$$ where $x_n$ is unknown. Therefore I ...
275 views

### 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,...
170 views

### A conjecture on six planes [closed]

When I read Cox's Theorem, and Clifford's Circle Theorem and Miquel six circles theorem, I found the conjecture as folowing. And I checked the conjecture by the Geogebra sofware, the conjecture is ...
586 views

### A problem of four curves

This is a generalization of my previous question, a problem of a cubic and six conics. Let a curve $(K)$ of degree $m$ and three curves $(C_i)$ of degree $n$, for $i=1,2,3$. Let $(C_1)$ meets $(K)$ ...
431 views

### A cubic and six conics problem

I am an electrical engineer system. I live in Viet Nam. I am not a Mathematician. I construct and found a problem as follows: Let a cubic, and five conics $(C_1)$, $(C_2)$, $(C_3)$, $(C_4)$, $(C_5)$. ...
466 views

### What is the Status of Borel conjecture today?

Let me recall the conjecture: $M$ and $N$ two aspherical closed $n$-manifolds with isomorphic fundamental groups, then $M$ and $N$ are homeomorphic.
218 views

### Is this a proof of the Hardy-Littlewood inequality? [closed]

V.V. Miasoyedov posted a paper to the arXiv claiming a proof of the Hardy-Littlewood conjecture $\pi(x+y) \le \pi(x)+\pi(y)$. It seems a bit off, and not only because the conjecture is widely believed ...
1k views

### A conjecture based on Wilson's theorem

Definitions: Lagrange's theorem implies that for each prime $p$, the factors of $(p − 1)!$ can be arranged in unequal pairs, with the exception of $±1$, where the product of each pair $≡ 1 \pmod p$. ...
37 views

### On a conjecture about Riemannian metric with positive sectional curvature [duplicate]

What is the last status of the following conjecture? Is it still open? What partial or similar results are known up to now? Conjecture: $S^2\times S^2$ admits a Riemannian metric with positive ...
567 views

203 views

### A conjecture on the prime counting function

I was thinking about the Second Hardy-Littlewood conjecture for quite sometime (some of my posts are related to this). In one of my earlier post I conjectured that the inequality ($\pi(x)$ denotes the ...
2k views

### Arctangents of odd powers of the golden ratio

While trying to answer this MSE question, I found that arctangents of many odd powers of the golden ratio $\varphi=\frac{1+\sqrt5}2$ are expressible as rational linear combinations of arctangents of ...
184 views

243 views

### Is the Tate conjecture known for etale covers of products of curves

Let $X$ be a (smooth projective geometrically connected) surface over a finitely generated field $k$. The Tate conjecture predicts that, for $l$ a prime number invertible in $k$, the Chern class map ...
187 views

### If there are two primes at an even distance $k$ is there another disjoint pair of primes also at distance $k$?

Suppose $p,q$ are two primes at even distance $k$. Must there necessarily exist a different pair $p',q'$ composed of entirely different numbers such that $p'$ and $q'$ are also at distance $k$? Edit: ...
124 views

### Primality Criterion for Specific Class of Numbers of the Form $k\cdot b^n-1$

Let $N=k\cdot b^n-1$ where $b$ is an even integer , $3\nmid b$ , $3\nmid N$ , $k \equiv 1,5 \pmod{6}$ , $k< b^n$ and $n>2$ . Let $S_i=P_b(S_{i-1})$ with $S_0=P_{k\cdot b/2}(P_{b/2}(4))$ , ...
113 views

336 views

### 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 ...
299 views

### Vaught conjecture for uncountable languages

Recall Vaught conjecture: the number of countable models of a first-order complete theory in a countable language is finite or $\aleph_0$ or $2^{\aleph_0}.$ Now let $\lambda$ be an uncountable ...
833 views

We know the following facts: (1) For all $1\leq n\leq 2$ the equation $x_{1}^{n}+x_{2}^{n}=x_{3}^{n}$ has a solution in $\mathbb{N}$. (2) For all $3\leq n$ the equation $x_{1}^{n}+x_{2}^{n}=x_{3}^{n}... 0answers 400 views ### Graphs with graphic imbalance sequences Let$G$be simple undirected graph and$e=uv\in E(G)$. The imbalance of the edge$e$is the value$imb(e)=|d(u)-d(v)|$. Let$M_{G}$denotes the imbalance sequence (or more correctly, multiset of ... 1answer 348 views ### An analogue of the Bass-Quillen conjecture with power or Laurent series The famous Quillen-Suslin theorem (formerly known as Serre's problem/conjecture) states that every projective module over$k[x_1,\dots, x_n]$is free for$k$a field. Replacing$k$by a more general ... 1answer 259 views ### An elementary expression for$_3F_2(1,1,9/4;2,2;-1)$Consider the following series: $$S=\sum_{n=1}^\infty\frac{(-1)^n\ \Gamma\left(\frac{5}{4}+n\right)}{n^2\ \Gamma(n)}.$$ It can be expressed in terms of a hypergeometric function: $$S=-\frac{5}{16}\... 1answer 423 views ### A conjecture on intersection of some intervals. It was proved here that if a\in \mathbb{N}_{\geq3} then$$\bigcap_{i = 1}^{a} \bigcup_{j = 0}^{i-1} \left[\frac{1+aj}{i},\frac{a(j+1)-1}{i}\right] = \varnothing \tag{1}$$It may be conjectured ... 7answers 2k views ### How closed-form conjectures are made? Recently I posted a conjecture at Math.SE:$$\int_0^\infty\ln\frac{J_\mu(x)^2+Y_\mu(x)^2}{J_\nu(x)^2+Y_\nu(x)^2}\mathrm dx\stackrel{?}{=}\frac{\pi}{2}(\mu^2-\nu^2),$$where$J_\mu(x)$and$Y_\mu(x)$... 2answers 312 views ### A sequence based on Catalan–Mihăilescu problem It was conjectured by Catalan in 1844 that the only solutions of the equation$x^a-y^b=1$over variables$a,b,x,y\in\mathbb{N^+}$are trivial ones:$3^1-2^1=1$and$3^2-2^3=1$. The conjecture was ... 1answer 854 views ### 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$S$,$...
Consider a symplectic manifold $(M,\omega)$ and the space of almost complex structures. These are $J:TM\to TM$ with $J^2=-\text{id}$. A given $J$ is $\omega$-tame when $\omega(v,Jv)>0$, and $J$ is \$...