Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [conjectures]

For questions related to conjectures which are suspected to be true due to preliminary supporting evidence, but for which no proof or disproof has yet been found

In mathematics, a conjecture is a conclusion or a proposition based on incomplete information, for which no proof has yet been found. There are many famous conjectures. Some of them have been proved, in which case they're technically no longer conjectures, and some have been disproved, and many others which still remain open, are yet to be proved or disproved. A few well-known conjectures are famous enough to have their own tag on this site: the Collatz conjecture, the ABC conjecture, and Goldbach's conjecture.

A list of some well-known conjectures can be found on Wikipedia.

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Solving a high school conjecture

Right, so this was something I stumbled upon whilst looking at forms of the golden ratio (if you replace x with one in the diagram above then you get phi) and then I wondered about what if you messed with the value of x, did a massive amount of…
Alex Robinson
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Mathematical conjectures believed to be false

I just came about the Firoozbakht's conjecture, and read that it is believed to be wrong, as it would contradict some heuristic methods. However, the conjecture is numerically verified for $p_n<10^{18}$. Are there other examples of mathematical…
Mario Krenn
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Prove a conjecture, balls in boxes, n steps

My uncle gave me the following problem to work on (just for fun), he doesn't know whether the problem has a solution. I haven't been able to solve it and I give up, I don't think my current knowledge is enough to solve it. Problem statement:…
untreated_paramediensis_karnik
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Conjecture about divergent periodic summations of odd functions

$$f(x)=\lim_{m\to\infty}\frac{\sum_{n=-m}^m(x-n)^{1/3}}{\sum_{n=-m}^m(1-n)^{1/3}}\stackrel{?}{=}x$$ I had a 'proof' but I made the simple mistake of assuming 2 limits could be swapped, so I only really proved that $f(x)=x$ for $x\in[-1,0,1]$, which…
Jacob Claassen
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An iteration formula I found (please don't jump at me if it's already been discovered)

$\sin^2 \theta$"> Where the modulus-like symbol actually denotes iteration of a radical function. Sorry for the messy work everyone- I am new to this stuff, and I literally just found this iteration formula like 15 minutes ago. $X[i]$ starts as…
Avtarás Karîm Elymés̱er
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Conjecture about special grid of numbers

Consider you have created grid of numbers like following image starting from any positive integer (in this case 8) To create such grid, follow this steps; Pick a number greater than one and write down $n, n-1, n-2, ..., 1$ as column…
yasar
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A question about Brown Numbers $(m, n) : n! + 1 = m^2$

So I recently looked at a video on YouTube by Numberphile which is accessible down below: Brown Numbers $-$ Numberphile The video was about so-called numbers called Brown Numbers. These types of numbers are a pair of integers $(m, n)$ such that $$n!…
Mr Pie
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poincare conjecture understanding

I have knowledge of basic school math, and in colleges I have read calculus (mostly forgotten now). I need to understand poincare conjecture, and hence I need to study a lot of things. I need to know from you what I should learn step by step to…
debnath
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Where's the list of connections of conjectures list on wikipedia?

Where's the list of connections of conjectures list on Wikipedia? There's an OEIS sequence that partially connects Collatz and Goldbach, as 2 mod 4 numbers having Goldbach partitions formed via it's members, should imply a Goldbach partition for the…
Roddy MacPhee
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Do all the zeroes of this arithmetic function occur at even integers?

Let $a(n)$ be the number of natural numbers $\le n$ which have an odd number of distinct prime factors. Let $b(n)$ be the number of natural numbers $\le n$ which have an even number of distinct prime factors. Conjecture: If $a(n) = b(n)$ then $n$…
Nilotpal Sinha
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Searching for a conjecture that is true until the 127 power of n.

I am searching for a mathematical conjecture that is true until something like n = 117, or n = 127, or a number close. It is an equality, a formula implying calcultations to the power of n, IIRC. What is the name of this conjecture ? Why do I…
Stephane Rolland
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