Conjecture Definition and 219 Threads

Has anyone ever heard of it, or better yet, done any research involving it? I'm doing some work with the conjecture, and I'm wondering if anyone could help me out.

The paper at this site "http://uts.awardspace.info" looked interesting to me, but would anyone else familiar with this problem, it's been around since the 30's, check it out and give an opinion.

can a conjecture be proved by 'empirical' means (observation) ?? i mean let us suppose that exists some functions named f_{i} (x) so \sum _{n=0}^{\infty} = \sum _{p} f(p) then an 'empirical' method would be to calculate the 2 sums and compare the error , let us suppose that the...

is there a proof for the goldbach's conjecture? that the every number can be written as the sum of three primes... or, every even integer can be written as the sum of two primes??

Let Q(\sqrt{k}), for some positive integer k, be the extension of the field of rationals with basis (1, \sqrt{k}). For example, in Q(\sqrt{5}) the element ({1 \over 2}, {1 \over 2}) is the golden ratio = {1 \over 2} + {1 \over 2}\sqrt{5}. Given an extension Q(\sqrt{k}), let B(n) denote the...

Detail attached Goldbach’s Conjecture and the 2-Way Sieve Intro: Mr. Hui Sai Chuen is an amateur mathematician born in May 1937 in the Canton province of China. After graduating with an engineering and construction degree, he proceeded to do research on architecture and material science...

Given A_1 = 3 \texttt{ and } A_n = A_{n-1}^{2} -2; is there a way to prove the following: \prod_{i=1}^{n}A_{i} = F_{2^{n+1}} or if someone has already proven this, can you give the reference?

[SOLVED] poincare conjecture http://en.wikipedia.org/wiki/Solution_of_the_Poincar%C3%A9_conjecture The links to Perelman's original proof do not work. Can someone fix them please?

Hi, Homework Statement Just having some troubles with a proof i have been asked to do, (sorry for not knowing the math code) basically, f(1)=0, f(2)=1/3 and f(n)= ((n-1)/(n+1))*f(n-2) and I've come up with the conjecture that f(n) = 0 when n is odd, and = 1/(n+1) when n is even...

If a is a perfect square then a is not a primitive root modulo p (p is an odd prime). (from Artin's conjecture on primitive roots) http://en.wikipedia.org/wiki/Artin%27s_conjecture_on_primitive_roots This is what I know: suppose a = b^2 a is a primitive root mod p when , a^(p-1) congruent to 1...

Well, it's a conjecture to me because I don't know (yet) if it's true or false. Let |A|=n, where n is an infinite cardinal. Let B be the collection of all subsets of A with cardinality less than n. Then |B|=n. Is it true first of all? And will the proof be short or long?

Hi everyone! Is anyone able to find the demonstration of the following Mersenne conjecture? for j=3, d=2*p*j+1=6*p+1 divide M(p)=2^p-1 if and only if d is prime and mod(d,8)=7 and p prime and there exists integer n and i such that: d=4*n^2 + 3*(3+6*i)^2 This conjecture has...

Homework Statement Conjecture: If K=a union of subsets of G with K open then each subset in the union is open The Attempt at a Solution Can't really see the proof. In fact it's false as any non discrete topology have open sets which are a union of subsets whch may not be open.

Conjecture: If x and y are coprime and M <> 2 then x^2 + Mxy +y^2 = p^2 has integral solutions only for p = a prime or for products of such primes. Also if M is positive then both x and y are partial solutions for X^2 -MXY + Y^2 = p^2. Thus 3*3 +3*5 +5*5 = 49 and 9 - 3*8 + 8*8 and 25 - 5*8 +...

Ok first i'd like to note that I'm not good at mathematics and have a vague understanding of the conjecture. What i'd like to know though is what comes now that this has been solved by Perelman? What implications does this have?

LOGICAL SYSTEMS+NEW PRINCIPLES+ATTEMPT TO SOLVE COLLATZ CONJECTURE. First i would like to say that am honoured to share my thought with great people in here who always provide help.I will not say iam right or wrong.I hope this post will be aspark to good mindes. I have viewed the laws of...

Hi, i hope it is not a crack theory i had the idea when reading Ramanujan resummation, i believe that for a Dirichlet series which converges for Re (s) > a , with a a positive real number then we can obtain a regularized sum of the divergent series in the form: \sum_{n >1}a_{n}n^{-s}-...

Goldbach's Conjecture (Theorem??) Hi guys, I just need to know if Goldbach's Conjecture has been demonstrated or not! Thx! :D

Let a triangular number T(n) = n*(n+1)/2 be factored into the product A*B with A less or equal to B. Let gcd(x,y) be the greatest common divisor of x and y For each of pair (A,B) define C,D,E,F as follows C = (gcd(A,n+1))^2, D = 2*(gcd(B,n))^2, E = 2*(gcd(A,n))^2, F = (gcd(B,n+1))^2...

I know I've commented before about some of the amazing things that my co-workers have come up with like "Is Germany its own country?" The guy that believes dinosaurs are faked by Darwinists because "you can make anything you want out of a pile of bones", was talking about the tv show "Are you...

Every prime number > 3 could be written as a sum of a prime number and a power of two. p,q are primes, n is positive whole number ==> p = q + 2^n 5 = 3 + 2^1 7 = 5 + 2^1 = 3 + 2^2 11 = 7 + 2^2 13 = 5 + 2^3 17 = 13 + 2^2 19 = 3 + 2^4 23 = 7 + 2^4 29 = 13 + 2^4 31 = 23 + 2^3 37 = 29...

Now that we've all warmed up a bit... Let's try this little gem of a conjecture... Instead of 2^x - 3^y or 3^y - 2^x, which together can be represented as abs( 2^x - 3^y ) since all we care about are the positive solutions, where abs( ) is absolute value, instead of that, let's try...

Is Jacobian Conjecture still open for general case? who knows the recent progress on this problem, especially in the approach of Feyman graph? 3x.

Does the Poincare conjecture say: Consider a compact 3-dimensional manifold V without boundary. Poincare conjectured that The fundamental group of V is trivial => V is homeomorphic to the 3-dimensional sphere? It has been proved for all manifolds except 3. However Perelman completed a proof...

The main idea to prove RH through the HIlbert Polya conjecture , is finding a Hamiltonian H=p^2 V(x) (QM) , so its energies are precisely the imaginary parts of the Non-trivial zeros. Using the Von Mangoldt formula for the Chebyshev function, differentiating respect to x , and setting...

I have a mathematical conjecture. It has to do with physics, but I call it a mathematical conjecture because the cases I which I generalized into a conjecture were done purely mathematically, with no actual physical experimentation. Consider a perfect rectangular mirror which obeys the law...

I'm looking for the name of the optimistic conjecture that, if I remember correctly, conjectures the existence of a certain kind of connection between every branch of mathematics. I read about it in Singh's book on Fermat's last theorem. Fueled by the enthusiasm following the discovery of a...

After studying Cesaro and Borel summation i think that sum \sum_{p} p^{k} extended over all primes is summable Cesaro C(n,k+1+\epsilon) and the series \sum_{n=0}^{\infty} M(n) and \sum_{n=0}^{\infty} \Psi (n)-n are Cesaro-summable C(n,3/2+\epsilon) for any positive epsilon...

Hey, i was reading about the Collatz conjecture, where, if you take a integer, divide it by 2 if its even and triple it then add one if it's odd, and do it over and over again, the result would be one. I was thinking, "wouldnt it have the same effect if you didnt triple odd numbers?" am i wrong?

if g(s)= \sum_{n=1}^{\infty} a(n) n^{-s} Where g(s) has a single pole at s=1 with residue C, then my question/conjecture is if for s >0 (real part of s bigger than 0) we can write g(s)= C(\frac{1}{s-1}+1)-s\int_{0}^{\infty}dx(Cx-A(x))x^{-s-1} of course A(x)=\sum_{n \le x}a(n)...

I was under the impression that Goldbach's Conjecture is still an open question in mathematics. Then what is it that the following three papers claim to do? (http://arxiv.org/ftp/math/papers/0609/0609486.pdf" ) Thanks for clearing up my confusion.

What is the poincare conjecture in layman's terms?

Greetings, I'm far from a skilled mathematician and I was wondering what greater minds than mine thought of Perelman's proof of the Pointcare conjecture. Also, if you could offer a brief explanation of the conjecture it would be very much appreciated. Here is a link to a bried article on...

http://arxiv.org/abs/hep-th/0610051 On cosmic natural selection Alexander Vilenkin 4 pages "The rate of black hole formation can be increased by increasing the value of the cosmological constant. This falsifies Smolin's conjecture that the values of all constants of nature are adjusted to...

Hello everyone, I'm confused on the directions. It says, Evalute the sum, for n = 1, 2, 3, 4, and 5. Make a conjecture about a formula for this sume for general n, and prove your conjecture by mathematical induction. This is the sum and my work...

After reading the article on Poincare's conjecture in the Economist, I became curious about simplified 3-dimensional objects. Excerpt: Let's take a cube and simplify it into a circle. Could we then use equations ment for circles for the simplified shape, ie calculate the cube's surface...

Is anything more known about Legendre's conjecture that there is a prime between n^2 and (n+1)^2 for positive integers n than what appears on MathWorld? MW says that a prime or semiprime always satisfies this, and that there is always a prime between n and n^{23/42} (21/42 would be equivilent...

HELLO, IN A LINEAR EQUATION OF THE FORM, X2 + Y2 + Z2 + D = 0 CAN THE PARAMETER BE -D WHERE t = parameter = -D and V = direction vector and Vt = <at, bt, ct> It seems as if it is...but I can't seem to prove it. HELP HELP HELP HELP

Perelman, Poincare Conjecture solved now?? Seems that this guy has solved the Poincaré Conjecture: http://en.wikipedia.org/wiki/Grigori_Perelman He is supposed to get the Fields Medal in Madrid this year, in the next international congress of mathematics. But it is likely that he won't...

1*1 1*3 2*2 3*1 1*5 2*4 3*3 4*2 5*1 1*7 2*6 3*5 4*4 5*3 6*2 7*1 * * * etc. If we go on constructing the pattern of numbers above, will each row contain atleast 1 product of two odd...

Can someone tell me when Grimm's conjecture (http://mathworld.wolfram.com/GrimmsConjecture.html) was formulated? I can't find any sources on that, and I don't have Guy's book.

Announced in http://www.intlpress.com/AJM/p/2006/10_2/AJM-10-2-165-492.pdf" . Differential Geometry meets Geometric Surgery on three-manifolds; Perelman clarified and (perhaps) corrected. A COMPLETE PROOF OF THE POINCAR´E AND GEOMETRIZATION CONJECTURES – APPLICATION OF THE...

Is "Berry Operator"... H=-i\hbar(x\frac{d}{dx}+1/2) the operator which give all the solutions of \zeta(1/2+iE_{n})=0 ?..it seems too easy to be true...:eek: :eek:

In an anlaogy with the Euler product of the Riemann function we make: \prod_{p}(1+e^{-sp})=f(s) of course we have that: f(p1+p2+p3)=f(p1)f(p2)f(p3) f(x)=exp(-ax) if Goldbach Conjecture is true then p1+p2= even and p5+p6+p8=Odd for integer n>5? then this product should be equal to...

I have a new conjecture re triangular numbers that I think is fascinating. Conjecture For any two integers a and b such that ab is a triangular number, then there is an integer c such that a^2 + ac and b^2 + bc are both triangular numbers. Further, (6b-a+2c)*b and (6b-a+2c)*(6b-a+3c)...

My question is...could the Hilbert-Polya conjecture if true prove RH (Riemann Hypothesis) i mean let,s suppose we find an operator ( i found a Hamiltonian with a real potential that gave all the roots of \zeta(1/2+is) ) in the form: R=1/2+iH with H self-adjoint so all the "eigenvalues"...

Ok my thread seems to have gone into a black hole. The existence of such a number would disprove Andrica's conjecture.

Could someone lay down, in layman's terms, The Poincare Conjecture? Lol, is this even possible?

All the roots of a real function f(x) are real unless. 1.K(x) is a Polynomial of degree k 2.f(x)=exp(g(x)) where g(x) is different from ln of something 3.f(z) with z=u+iv is invariant under the transformation of v=-v with f(u+iv)=F(u-iv).. 4.the function f includes some of the functions...

Bear with me. I'm new to forum and don't yet know all protocol. My question concerns twin primes. The previous thread on this topic seems to be closed. My question is this: When considering the Twin Primes Conjecture, has anyone researched the idea that (heuristically speaking) there is...