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

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6
votes
0answers
210 views

Does the set of $m \in Max(ord_n(k))$ for every $n$ without primitive roots contain a pair of primes $p_1+p_2=n$?

I have made the following observation: for those n even numbers that do not have primitive roots modulo n ,$Pr(n)$, the set $M(n)$ of those $k$ having a maximum multiplicative order $ord_n(k)$ ...
4
votes
2answers
74 views

Conjecture: only one even Fibonacci term divided by two gives a prime: $F(9) = 34 = 2 \times 17$

Every Fibonacci term $F(3n)$ is divisible by two $F(3) = 2$ $F(6) = 8$ $F(9) = 34$ $...$ After seeking Fibonacci tables factorization until $F(10000)$, for every term $\frac{F(3n)}{2}$, it ...
5
votes
1answer
145 views

Conjecture about the product of the primitive roots modulo a prime number ($\prod Pr_p$)

While I was learning about the primitive roots modulo $p \in \Bbb P$ (I will call $Pr_p$ to the complete list of the primitive roots module $p$) and having in mind the conjecture explained in this ...
-3
votes
1answer
426 views

Is this attempted proof of ABC conjecture correct [closed]

This mathematician claims that he has tackled ABC conjecture! He uses induction and simple inequalities to achieve the result. Is this some serious stuff or is there a basic flaw in the reasoning?
2
votes
3answers
113 views

Why is it that if you square two prime numbers and add them, you get a number that is even and is not a perfect square?

If you do $x^2 + y^2 = n$ where $x$ and $y$ are both prime numbers and are both greater than $3$, why is $n$ always an even number that isn't a perfect square?
11
votes
2answers
294 views

Yet another conjecture about primes

Let $\mathcal{N}(n)$ be the next prime greater than $n$. Conjecture: $\mathcal{N}(n!)-n!\:$ is either $1$ or a prime. It holds for n=1 to 99 and the expression is 1 for 3,11,27,37,41,73,77 and ...
6
votes
2answers
126 views

The conjecture that no triangle has rational sides, medians and altitudes

I have found a conjecture that there is no triangle whose sides, medians, altitudes and area are all rational. I figure that someone must have already found such a triangle if one existed and yet I ...
3
votes
3answers
896 views

Result of solving an unsolved problem?

I was mulling over currently unsolved problems in mathematics (as I, and many others, find them quite interesting) and began to wonder what would happen if these problems were to be solved. I know ...
2
votes
2answers
36 views

Algorithmic procedure to establish the possibility of finding a proof of a conjencture

I was always puzzled by these conjectures which can be stated quite simply, yet finding a proper proof is a monumental task even for the most brilliant mathematicians . Consider the following ...
5
votes
1answer
194 views

Euler's totient and divisors count function relationship when $[(\frac{\varphi(n)}{2}+1)\cdot(\frac{\tau(n)}{2}+1)] = n$

I am studying the Euler's totient function $\varphi(n)$ and the divisors count function, $\tau(n)$, also named $d(n)$, and recently opened a question (link here) about the following condition: ...
1
vote
2answers
51 views

Prove that $\det(A) \cdot v \, A^{-1} = \det(A+uv) \cdot v \, (A+uv)^{-1}$.

Let $A$ be a $n \times n$ matrix, $u$ a $n \times 1$ matrix and $v$ a $1 \times n$ matrix. If $A$ and $(A+uv)$ are invertible, prove that $$ \det(A) \cdot v \, A^{-1} = \det(A+uv) \cdot v \, ...
1
vote
1answer
83 views

Euler's Totient function $\forall n\ge3$, if $(n-\phi(n)) = \sqrt{n}\ $,$\ $then $(n-\phi(n)) \in \Bbb P$

Recently I opened a question about what it might be a new property of Euler's Totient function. I am still studying the Totient function and I found another interesting relationship, it is very ...
17
votes
2answers
529 views

Euler's Totient function $\forall n\ge3$, if $(\frac{\varphi(n)}{2}+1)\ \mid\ n\ $ then $\frac{\varphi(n)}{2}+1$ is prime

While I was studying Euler's Totient function, $\varphi(n)$, I stumbled upon the marvelous book "Index to Mathematical Problems, 1980-1984" By Stanley Rabinowitz. In this page of the book (link to ...
3
votes
2answers
72 views

Conjectured diagonal Ramsey numbers

While doing some reading on the Wikipedia page for Ramsey numbers, I stumbled upon OEIS sequence A120414, which lists the allegedly conjectured values of the diagonal Ramsey numbers $R(n,n)$. I ...
4
votes
3answers
92 views

Given an odd $x$ there is an $m,n$ such that $2^n + 1 = 3^m x$?

I'm curious about this question: Is it true that for any odd number $x\in 2\mathbb N + 1$ there exists numbers $m,n\in \mathbb N \cup \{0\}$ such that $$2^n+1 = 3^mx$$ Edit: I'm not trying to make ...
0
votes
1answer
49 views

Binary Representation of the Collatz Conjecture

What is the benefit of looking at the binary representation of the collatz conjecture. I know that it makes the computation easier because there is really one operation involved which is multiplying ...
7
votes
2answers
393 views

Trying mathematical induction with $3n+1$ conjecture

Collatz's Conjecture is also known as the $3n+1$ conjecture. Well I thought since the conjecture is dealing with natural numbers so we might as well try mathematical induction and see why it doesn't ...
0
votes
1answer
85 views

A question about the $3n+1$ conjecture

So I know that if you take any even number $n$ that is a power of $2$ like $32 = 2^5,16=2^4$ or $64=2^6$ we will keep dividing by 2 until we reach 1. and so all the steps will be $\frac{n}{2}$ and we ...
2
votes
2answers
84 views

Can I demonstrate a proposition without a rigorous proof?

Writing a paper, I want to declare a certain proposition, but is only supported by other research's empirical result. In this sort of case, what can I name to my argument in my paper? CONJECTURE is so ...
1
vote
1answer
98 views

Asymptotic behavior of the zeros of the digamma function

The gamma function has just one extremum on each interval $(k,k+1)$, where $k$ is a negative integer. These extrema occur at the zeros of the derivative of the gamma function. Let $z_n$ denote the ...
7
votes
1answer
151 views

Power towers of $2$ and $3$ - looking for a proof

Let $\uparrow$ denote the right-associative exponentiation operator: $a\uparrow b\uparrow c=a\uparrow(b\uparrow c)=a^{b^c}$ There is a sequence $A248907$ recently submitted to OEIS (see also ...
0
votes
1answer
26 views

Prove conjecture using premises

I have three premises with me defined: $(B \land L) \implies A$ $(A \land D) \implies \lnot H$ $\lnot J \implies (D \land \lnot H)$ I need to prove the following conjecture with the help ...
0
votes
1answer
114 views

Legendre's Conjecture!

This is my last attempt to the Legendre's Conjecture: based on my first one, it's not that difficult to follow, I'm not using logical manipulation or something like this, it's all about inequalities ...
0
votes
4answers
76 views

In the Collatz function, why does $2^k-1$ reach $3^k-1$ after $2k$ steps, and could it be used to find divergent trajectories?

If you start calculating the Collatz function from an integer of the form $2^k-1$, you will reach $3^k-1$ after $2k$ steps. So, it is possible to pick a starting value that continuously zig-zags ...
1
vote
2answers
47 views

In the Collatz function, why $3^{2k}-1$ and $3^{2k-1}-1$ always share the same trailing trajectory?

Why are the trajectories always the same for numbers of the form $3^{2k}-1$ and $3^{2k-1}-1$ for the Collatz function? For example, let $k = 3$. So, $3^6-1 = 728$ and $3^5-1 = 242$. The trajectories ...
4
votes
3answers
101 views

Generalizing conjecture of Bertrand

Joseph Bertrand's conjecture for primes from 1845, $\;p_{n+1} < 2p_n$, proved by Chebyshev 1852, can be generalized as follows: $$\forall a\in\Bbb Z_+\exists N\in\Bbb Z_+:(n\ge N\implies\exists ...
0
votes
1answer
45 views

Has this partial result about Legendre's Conjecture been proved?

I'd like to know if it has been proved this "partial result" about the Legendre's Conjecture: (1) There are infinitely many $n$ such that there's a prime in $(n^2, (n+1)^2)$ Thanks!
-4
votes
1answer
455 views

$k$-tuple conjecture.

Time is running out Suggest notation for Steps 1 and 2. Earn the bonus. For each $k\in\mathbb{Z^{+}}$. Step 1: Create a list $(1,1,1,1...,1)$ of length $k^2+2k$. Step 2: For all n: $1< n \leq ...
6
votes
0answers
103 views

Possibly New Prime Conjecture

I was in the midst of proving a conjecture when I came across an observation that led me to forming a potentially new conjecture. The conjecture goes as follows: Any given sum of twin primes ...
2
votes
1answer
46 views

Explanation for relationship between hypotenuse segments and leg lengths?

|` | ` x | ` | ` c a | z /` | / ` y |_/ ` |/|_____` b I'm new to this SE, but I have an SO account, so hello! Can ...
0
votes
1answer
98 views

How to convert an object into a sphere?

I'm not sure if I understand it enough, but doesn't the Poincare conjecture prove any shape can be turned into a sphere? How would I go about transforming such an object? Like let's say I have a ...
2
votes
1answer
415 views

Proof of Andrica when Assuming Oppermann

Proof of Andrica's conjecture by assuming Oppermann's conjecture. Oppermann's conjecture: $$n\geq2\wedge\pi\left(n^{2}-n\right) < \pi\left(n^{2}\right) < \pi\left(n^{2}+n\right).$$ ...
18
votes
1answer
897 views

List of generally believed conjectures which cannot all be true

There are some conjectures which most leading experts believe in albeit no one can prove it yet. For example: $\mathcal{P} \neq \mathcal{NP}$, the Riemann hypothesis or the Collatz conjecture. My ...
3
votes
1answer
227 views

Prove or disprove this upper bound on chromatic number.

Let $G$ be a simple connected finite graph and let $v \ge 4$ be the number of vertices, $E$ the number of edges, $\chi(G)$ the chromatic number , $\omega(G)$ the clique number and $\Delta$ the ...
7
votes
3answers
419 views

On progress in mathematics: some long-open problems and long-standing conjectures

I would like to ask a question here on Math Stack Exchange taking inspiration (and therefore combining) from two well-known threads on MathOverflow: (1) Not especially famous, long-open problems which ...
5
votes
1answer
104 views

Two conjectures regarding $\varphi(n)$

There is a famous unsolved problem called Lehmer's Totient Problem which states that, $\varphi(n)\mid n-1 \implies n$ is a prime. Where $\varphi(n)$ is Euler's Totient Function. I was ...
25
votes
0answers
910 views

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 ...
6
votes
2answers
78 views

Conjecture about the powers of 2 in the prime factorizations of the series $a_n = n(n+1)(n+2)$

I found the following law and would like to know what do you think about it and if anyone can explain why this is so. Also, is this already known and proven? Consider the following series: ...
1
vote
1answer
94 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
116 views

Conjecture on the value of limit and related primality testing

Just I made a curious conjecture when I was playing with my calculator. We will use $\displaystyle\prod_{i=1}^n p_i$ where $p_i$ is the $i$-th prime. Then I have noted that, $$\left\lvert\cos ...
2
votes
0answers
78 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 ...
3
votes
1answer
194 views

How to submit a conjecture for review?

I was recently attempting to solve one of the more known, already proved, problems in mathematics when I stumbled across an observation I thought might be worth digging into further. Unfortunately I ...
2
votes
0answers
149 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 ...
14
votes
2answers
420 views

A conjecture concerning primes and algebra

A monoid morphism $\psi:\mathbb Z_+\!\!\rightarrow\mathbb Z_+$ is defined by an arbitrary function $f:\mathbb Z_+\!\!\rightarrow\mathbb Z_+$ and defines a group homomorphism $\varphi:\mathbb ...
79
votes
23answers
2k views

Open mathematical questions for which we really, really have no idea what the answer is

There is no shortage of open problems in mathematics. While a formal proof for any of them remains elusive, with the "yes/no" questions among them mathematicians are typically not working in both ...
132
votes
1answer
7k views

A variation of Fermat's little theorem

Fermat's little theorem states that for $n$ prime, $$ a^n \equiv a \pmod{n}. $$ The values of $n$ for which this holds are the primes and the Carmichael numbers. If we modify the congruence ...
4
votes
4answers
808 views

Can decimals/fractions be odd or even? [duplicate]

At school I asked the question and I kept wondering "Can fractions or decimals be odd or even?"
5
votes
1answer
114 views

At most n functions

Some background: I was trying to solve the functional equation f(f(x))=sin(x). I realized that $f(\pi n)$ is a root of f for all integers n, because $f(f(\pi n))=\sin(\pi n)=0$. Thus, we can write f ...
2
votes
2answers
164 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
votes
1answer
90 views

A Conjecture on The Generalization of Quadratic Reciprocity Law

Is there any way to prove the following conjecture regarding the Generalization of Quadratic Reciprocity Law. The statement being, $$ \left(\dfrac{a_1}{a_2}\right)\left(\dfrac{a_2}{a_3}\right) ...