Conjecture Definition and 231 Threads

I'm sure there are mistakes here so criticism is welcome. In the unlikely event someone would like to sponsor my article for ArXiv, please let me know. http://www.non-ducor.com/fj/Algebraic_proof_of_Fermats_conjecture_001.png...

Homework Statement prove or disprove the following conjecture: If n is a positive integar, then n^2 - n +41 is a prime number Homework Equations no, just prove or disprove The Attempt at a Solution I think one possible answer may be there is no factorization for this except...

The prime numbers are the multiplicative building blocks of the integers. Even so, their distribution escapes all methods of rationalization. As with building a pyramid, the primes are most densely distributed near zero, the point of origin, and as we move towards larger numbers the primes are...

Given polynomials of degree n > 2, such that they have the form of p(x) \ = \ x^n \ + \ a_1x^{n - 1} \ + \ a_2x^{n - 2} \ + \ a_3x^{n - 3} \ + \ ... \ + \ a_{n - 2}x^2 \ + \ a_{n - 1}x \ + \ a_n. And \ \ all \ \ of \ \ the \ \ a_i \ \ are \ nonzero \ integers \ (which...

Hello there everyone! I've written a lovely little program to go through the tedious process of testing numbers in the "If odd 3n+1; If even n/2; Repeat." scenario. It then saves all of the numbers, starting with the integer being tested, and ending with "1" in a file of the form...

I have conjectured that two different waves in the same region, will not exactly result in the superposition, or addition of both waves independently. The logic: Every point in a region which a wave propagates has a position, and an acceleration which partially, if not totally, depends on the...

Hey guys, I saw these just showed up on arXiv, published by some unknown who claims to have invented his own number system and is not affiliated with any academic institutions. What do you make of this? http://arxiv.org/abs/1110.3465 http://arxiv.org/abs/1110.2952

Is it true that \int_0^1 f(x) dx \in \mathbb{Q} \Rightarrow \int_0^1 x f(x) dx \in \mathbb{Q} ? (Suppose f(x) integrable as needed) I thought of this conjecture yesterday and still couldn't prove it, I tried using integration by parts to relate it to the original, but didn't...

Hey, this is my first post, so... Hello everybody! I've been looking into the Collatz conjecture, and like most mathematically minded people, been completely absorbed by it. I'm looking to bounce some ideas off other people, kind of a peer review of a couple things if you will. I'll be the...

By supposing there is a solution to Fermat's Last Theorem then according to Frye you can create an elliptic curve that isn't modular. Taniyama-Shimura says that all elliptic curves are modular, so in proving that that Frye curve is not modular which was done by Ribet don't you disprove the...

Hi there PF My question here is: Is the Bagger-Lambert-Gustavsson action (http://en.wikipedia.org/wiki/Bagger%E2%80%93Lambert%E2%80%93Gustavsson_action) a way of proving the "M-theory as a matrix model: a conjecture" (http://arxiv.org/abs/hep-th/9610043) or is it a different approach? And how...

Hi all, I've developed a new sieving method that I believe provides a tight lower bound for the counting of certain kinds of primes. I'm 99% sure my solution works, and if so, it would allow the solution of many kinds of problems in additive number theory. The sieving method came out of...

Fix some constant 0<\alpha \leq 1, and denote the floor function by x\mapsto [x]. The conjecture is that there exists a constant \beta > 1 such that \beta^{-n} \sum_{k=0}^{[\alpha\cdot n]} \binom{n}{k} \underset{n\to\infty}{\nrightarrow} 0 Consider this conjecture as a challenge. I don't...

CONJECTURE: Subtract the Absolute Values of the Stirling Triangle (of the first kind) from those of the Eulerian Triangle. When row number is equal to one less than a prime number, then all entries in that row are divisible by that prime number. Take for instance, row 6 (see below). The...

If we have n (possibly unequal) resistors, we can combine them in various ways to produce a device with two terminals. In many cases, the equivalent resistance of this device can be found by repeatedly breaking the circuit down into parallel and series parts. Conjecture: n=5 is the lowest for...

Let p,q be two different primes from 5 onwards (not 2 or 3). Let p be the biggest of the two. The difference of squares p^2 - q^2, since p,q are both odd, is always a multiple of 8 (easy to prove). So take the integer k = (p^2 - q^2) / 8. It turns out that k seems to be (says friend computer)...

I was doing some thinking about good old Goldbach and noticed that every pair of primes was the same distance away from half of the even number. For example, 3 + 5 = 8 and |4 - 3| = 1 = |4 - 5| 3 + 13 = 16 and |8 - 3| = 5 = |8 - 13| 7 + 17 = 24 and |12 - 7| = 5 = |12 - 17| 19 + 23 = 42...

Limiting ourselves to N... Conjecture: (sqrt (16x + 9) - 1)/2 = y | 2y^2 + 2y - 3 = z^2 for x = a Sophie Germain Triangular Number, which is recursively defined as: a(n)=34a(n-2)-a(n-4)+11 First 11 values (I have not checked further as I would be very surprised if this equivalency...

I have read in the past that having a base 12 number system is superior to a decimal system because of the number of factors that 12 has. For instance we essentially use base 12 for time, it's better to have a 60 minute hour than a 100 minute hour as there are more 'convenient chunks' or factors...

Hello; I don't know how to prove this conjecture I've made; For the polynomial equation -\sum_{n=0}^{\infty}k^{n}=0 there exist no real solutions greater than 2, no matter how large the value of n. How do I show that this is true? If it's a little unclear, what I mean is, for example, if...

I was wondering if one of the consequences of the Elliott-Halberstam conjecture would imply the Riemann Hypothesis (RH) or the Generalized Riemann Hypothesis (GRH)? Or at least if there is a connection between the Elliott-Halberstam conjecture and RH or GRH? I ask because the...

Considering that the smallest particles in nature are supposed to be strings, which are donut and line shapes. And the poincare conjecture says the simplest shape in nature is a sphere. wouldn't it make sense that the true fundamental particles are sphere shaped and that if they combine to form...

Attached is the proof.

What are usual tips in conjecturing formulas for math induction if I am given a certain sum of sequence? Thank you.

Hey, I am a junior in physics at penn state and am currently in a philosophy class. We have an assignment to argue a question of conjecture(my professor specified he wanted a problem of the "did/does anything actually happen") in our fields(majors). I am kind of struggling to find a good topic...

Spin behaves as if it is one dimensional, along any axis you select. This behavior would be just what one expected from a vector which, owing to spontaneous dimensional reduction, lived in a one-dimensional world. But according to several approaches to QG, very small "things" or degrees of...

Conjecture: Consider any group with an even number of people where each member is connected to any other through some chain of people. Then the original group can be split into groups where each member knows an odd number of people directly. Note: If the party is such that each member knows an...

(Dis)proof of Riemann hypothesis,Goldbach,Polignac,Legendre conjecture I'm just an amateur and not goot at english ^^;

i have the following conjecture about infinite power series let be a function f(x) analytic so it can be expanded into a power series f(x)= \sum_{n=0}^{\infty} a_{2n}(-1)^{n} x^{2n} with a_{2n} = \int_{-c}^{c}dx w(x)x^{2n} w(x) \ge 0 and w(x)=w(-x) on the whole interval (-c,c) in case...

SIMPLE PROOF OF BEAL’S CONJECTURE (THE $100 000 PRIZE ANSWER) Beal’s Conjecture Beal’s conjecture states that if A^x + B^y = C^z where A, B, C, x, y and z are positive integers and x, y and z are all greater than 2, then A, B and C must have a common prime factor. Examples...

SIMPLE PROOF OF BEAL’S CONJECTURE (THE $100 000 PRIZE ANSWER) Beal’s Conjecture Beal’s conjecture states that if A^x + B^y = C^z where A, B, C, x, y and z are positive integers and x, y and z are all greater than 2, then A, B and C must have a common prime factor. Examples...

I wonder if the Goldbach Conjecture could be extended, so that the even number halfway between two primes that differ by 4n + 2 can be written as the sum of two primes from pairs that differ by 4n + 2? This conjecture often fails for the first few numbers, but then seems to begin working. For...

Here is my proof of the 'Twin Prime Conjecture'.

I believe I have proved that there are an infinitude of twin primes using elementary algebra and a straightforward thought experiment. My proof will be sent shortly.

Hey there! I want to make myself familiar with Dirac's conjeture. Does anyone know a good source for it? I don't want to read his paper form the 50ies and hope there is a more pedagogical introduction of the topic... :) Thanks!

Conjecture: If P is odd, then there is one and only one number n in the set {1,2,3,...(P-1)} which satisfies the equation (32*n^2 + 3n) = 0 mod P an this number. Can anyone help me with a proof of this? If by chance this is a trival matter. I have gone further and determined 4 equations for...

Make a conjecture about the nth derivative of the function f(x)=e^(ax). This conjecture should be written as a self contained proposition including an appropriate quantifier. What is the last sentence saying to do. I know what a conjecture is but I am confused on what the book wants here.

hello! i would like to be able to understand and appreciate the proof of the poincare conjecture. i have some idea of where to begin, and my supervisor is going to help me out (i'm starting a master's in pure math and my supervisor does geometric analysis), but i was wondering if anyone here...

4=2+2, 6=3+3. Are there any other cases where an even number of the form 2p, where p is a prime, cannot be represented as the sum of two different primes?

Hello dear forum members I wanted to know where are the research on the Riemann hypothesis , the latest advances ,who are the currently leading experts and is now known that mathematics it requires for its resolution

Hi. I might just have something here. Please let me know if you have any questions or comments. Thanks. Andy Lee. leeaj@shaw.ca See proof at http://www.facebook.com/pages/Goldbachs-Conjecture-Proof/237054761999

a "Single String Conjecture"? -Feynman revisited Do we all remember Feynman's "Single Electron Conjecture" that states, basically, that a single electron moving back and forth in time could "fill in the gaps" on every electron ring around every atom in the universe? Well, assuming Superstring...

Homework Statement The Goldbach Conjecture: Every even number greater than 2 is the sum of 2 primes Consider P(n) = (n is congruent to 3mod4) Then g(n) ={0 if n = 1 or 2n is a sum of 2 primes 1 if 2n is not a sum of 2 primes and P(n) is true...

i've got the following conjecture about XI function, the following determinant p_n(x) = \det\left[ \begin{matrix} \mu_0 & \mu_1 & \mu_2 & \cdots & \mu_n \\ \mu_1 & \mu_2 & \mu_3 & \cdots & \mu_{n+1} \\ \mu_2 & \mu_3 & \mu_4 & \cdots & \mu_{n+2} \\ \vdots & \vdots & \vdots & & \vdots \\...

Hi all, Tim Gowers has a list of possible Polymath projects up, where he mentions the Littlewood Conjecture: This states, informally, that all reals can be approximated reasonably well, in the sense that if we let the denominator of an approximation \frac{u}{v} grow, the error term becomes...

http://www-personal.ksu.edu/~kconrow/" I mean really read it, to where they understand it, not just to the point where their eyes glaze over? I see his site cited quite frequently, but I don't know if I've ever seen any critique. I admit, I was intimiitaded by his site at first. But...

I mean, according to my knowledge, Bertrand's postulate has already been proved, I've already read and understood one, but Paul Erdos, and a few other mathematicians have proved it using various methods. I just finished reading Ramanujan's proof. Its amazingly advanced, and really short. The...

A random walk can be defined by the following recurrence relation, X_{t+1} = X_t + \Delta X where \Delta X \sim \mathcal{N}(0, \sigma^2). At any time t1 \geq 0 a strategist may enter, and at any time t2 > t1 a strategist may exit. The resulting profit p is given by: p(t1,t2) = X_{t2}...

Can it be proven that the number of prime pairs with a difference of two (that is, primes separated by only one even number) approaches infinity?

"Of the numbers N>1, only 4 and 6 cannot be expressed as a sum of prime numbers with unique values."