Use this tag if your question is about a well-known conjecture or a conjecture of your own.

learn more… | top users | synonyms

3
votes
2answers
66 views

Prove that $\lim\limits_{x\to\infty} \frac{\Gamma(x+1,x(1+\epsilon))}{x\Gamma(x)}=0$.

I conjecture that for any $\epsilon>0$, we have $$ \lim_{x\to\infty} \frac{\Gamma(x+1,x(1+\epsilon))}{x\Gamma(x)}=0 $$ where $\Gamma(x,a) = \int_a^\infty t^{x-1}e^{-t} \mathrm{d}t$ denotes the ...
2
votes
2answers
108 views

Equal perimeters of squares and right angled isosceles triangles

Consider a square ABCD having length l and breadth. Now start folding the sides AB and AC so that the figure becomes something like this $$$$ All the vertical and horizontal folds/stairs are equal in ...
2
votes
1answer
41 views

Firoozbakht's conjecture and maximal gaps

In the Wikipedia article, it seems to me as if it's implied that it is enough to check the conjecture only for maximal gaps (numbers $n$ s.t. $\forall k<n:g_n>g_k$). I.e it holds that ...
1
vote
1answer
89 views

Conjecture: three or more decompositions into powers with a base differing by 1 means its a perfect power

If $$(i_1)^{a_1}(i_1+1)^{b_1}=n $$ $$(i_2)^{a_2}(i_2+1)^{b_2}=n $$ $$(i_3)^{a_3}(i_3+1)^{b_3}=n $$ where all the terms are positive integers and the groups ...
1
vote
1answer
163 views

Tangent at average of two roots of cubic with one real and two complex roots

I was able to easily prove that the tangent at the average of two roots of a real cubic polynomial passed through the third root of the function. But I have only done this for functions with three ...
0
votes
1answer
142 views

For all $n$, $9^n + 25^n - 1$ has a prime factor with $7$ in its decimal representation?

Let $x_n$ be a sequence of positive integers defined by $x_n=9^n + 25^n -1$ for all $n \ge 2$ I conjectured that there exists at least one prime divisor of $x_n$ which contains $7 $ in its decimal ...
11
votes
0answers
209 views
+50

On the problem of polynomial bijection from $\mathbb Q\times\mathbb Q$ to $\mathbb Q$

The question titled "Polynomial bijection from $\mathbb Q\times\mathbb Q$ to $\mathbb Q$" which was posed on MathOverflow attracted quite a lot of attention (and may be the question with most wrong ...
8
votes
0answers
274 views

Asymptotic FLT $\implies$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 ...
6
votes
0answers
90 views

Question regarding the status of Erdős' conjectures

Has Erdős' conjecture on arithmetic progressions or his conjecture on Sylvester's sequence been proven?
5
votes
0answers
109 views

Are $ut + 1$ and $ut + t + 1$ both prime for some t for any $u$?

Conjecture : For any natural number $u$, there is a natural number $t$ such that $ut + 1$ and $ut + t + 1$ are both prime. So we get a solution of the equation $$au - b(u+1) = -1$$ with prime ...
4
votes
0answers
107 views

What are the recent advancements in mathematics that an undergraduate can understand?

I am an undergraduate student of mathematics. I am interested to know the conjectures that are proved in the last, say 5 or 10 years. Or any other development. Preferably in pure mathematics. One of ...
3
votes
0answers
94 views

conjecture about prime numbers and distance between them

is there a name for this conjecture? Conjecture: given $p_n$ a prime number sequence where $p_1=2,p_2=3,\cdots$, then for all $n\in\mathbb{N}^*$ and $k\in\mathbb{N}$, holds that $\displaystyle ...
3
votes
0answers
373 views

Totient summatory function

Let $\Phi(n) = \sum_{k=1}^n \phi(k)$ be the totient summatory function. Here is an interesting conjecture I've made: The ratio $\Phi(n^2)/\Phi(n)$ is an integer only for $n=1,2,3,5$ and $6$. I made a ...
3
votes
0answers
66 views

A challenging non homogenous fractional inequality.

The following problem is a challenging generalization of several difficult inequalities, where none of the usual methods used in inequalities seems to work. I would like to know if someone has a ...
3
votes
0answers
82 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 ...
3
votes
0answers
312 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 ...
2
votes
0answers
67 views

A similar, but hopefully easier problem than Gilbreath's conjecture

Gilbreath's conjecture says that for every positive integer $n$, if we write out the first $n$ primes $2,3,5,7,11,13,\ldots,p_n$ take the differences between consecutive terms ...
2
votes
0answers
62 views

Is this a conjecture or an already existing one??

Does the following inequality hold? $p(n)\leq 2^n,$ where $p(n)$ is the $n$th prime. If this is true then it follows that: If $p(n)=p(m)^x+p(o)^y$, then $\max[x,y] \le n$.
2
votes
0answers
30 views

Decidability of $P = NP$?

(Please, don't sign this as duplicate of this question, they are not.) Is it possible, that the well-known $P=NP$ conjecture is undecidable in ZFC? Is there any result about this topic?
2
votes
0answers
63 views

Prove the inequality for composite numbers

Is it true that $c_m+c_n$ $>$ $c_{m+n}$ for all $m$, $n$ $\in$ $\mathbb{N}$? Though the result seems true, I can't get a solution. Even the bounds on $c_n$ obtained from Prime Number Theorem ...
2
votes
0answers
49 views

How to prove that every $l$ (such that $ 2 \leq l \leq \lfloor \sqrt{k^2+2n+1} \rfloor $) divides at least one of the following numbers?

$ k^2+2n, k^2, k^2+1, 2n, 2n+1$, (for some $n$) if $k$ is even and $0 < n < k$. I have no idea of how to prove that. I'm working on Legendre's conjecture. Update 1: Yes, for $n=0$ all $l$ ...
2
votes
0answers
159 views

Approximation to $\pi(x)$ conjecture.

A friend conjectured that $\left[\prod_{k=1}^{a_j <\sqrt{x}} \left(1-\frac{1}{a_k}\right)\right] x$ is usually closer to $\pi(x)$ than $\operatorname{Li}(x)$ is for some (fixed) sequence of ...
2
votes
0answers
79 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
57 views

Inequality with Euler's totient function

In A conjecture concerning primes and algebra on MSE, I defined a multiplicative function $\omega:\mathbb Z_+\!\!\to\mathbb Z_+$ with $\omega(p_n)=n$, for the $n$-th prime $p_n$. It was conjectured ...
1
vote
0answers
88 views

All about a failed conjecture.

Some months ago I made the following conjecture - Let $d(n)$ denote the number of divisors of $n $. Then let $N$ be a number such that $d(N)$ divides $N$ . Also let $I= \frac{N}{d(N)}$ which is ...
1
vote
0answers
156 views

Proving there exists prime numbers between the squares of prime numbers

Conjecture: $\forall $ $p_{n}$, $p_{n+1} \in \mathbb{P}$, $\:$ $p^2_{n+1} = p^2_{n} +\omega_{n} p_{n} + \phi_{n} : \phi_{n} , \omega_{n} \in \mathbb{N} $ and $ \phi_{n} < p_{n}$, $\:$ ...
0
votes
0answers
14 views

Counterexample to a generalization of Gilbreath's conjecture

Consider the arrays with "initial conditions" $L_1^1>0,\ L_{n+1}^1>L_n^1,\ L_1^{i+1}=1$ satisfying the recurrence $L_n^{i+1}\in\{L_n^i-L_{\large{\inf\{m\in\Bbb Z_{>n}:L_m^i\leq ...
0
votes
0answers
35 views

Which conjectures imply Standard conjectures?

My attention (around this question) arose from this "MO Question" in which Jakob says: The period and the Hodge conjecture imply the Standard conjectures. Is that true? Are there other ...
0
votes
0answers
113 views

Arithmetic progression and average of two prime numbers

Let $A=(a_n : n \in \mathbb{N})$ be the sequence given by: $$ \ a_n = a_1 + (n - 1)d,\quad a_1,\ d,\ n \in \mathbb N,\quad d\gt a_1,\quad \gcd(a_1,\ d)=1. $$ For all terms of $A$ greater than $\ ...
0
votes
0answers
29 views

A conjecture on the product of digits of a number

Define $(m,n)$ to be a special pair if $n=m \cdot Pd(n)$. Where $Pd(n)$ is the product of digits $n$. Then I have the following conjecture - For every $m$ with no digit of $m$ being $0$ , there ...
0
votes
0answers
21 views

Make a conjecture that $g(x)=\lfloor{kx}\rfloor$ for a particular value of k

Make a conjecture that $g(x)=\lfloor{kx}\rfloor$ for a particular value of k. I am thinking that it has to do with where k is a fraction or not but I am unsure how to write it out.