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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Conjecture about :$\frac{a}{\sqrt[4]{8(b^4+c^4)}}+\frac{b}{a+c}+\frac{c}{a+b}\geq\sqrt{\frac94+\frac32 \cdot \frac{(a-b)^2}{ab+bc+ca}}$

It's a conjecture . I combine two inequalities : Stronger than Nesbitt inequality and Stronger than Nesbitt's inequality $\frac{a}{\sqrt[4]{8(b^4+c^4)}}+\frac{b}{a+c}+\frac{c}{a+b}\geq\frac{3}{2}$ So now the conjecture : Let $a,b,c>0$ such that…
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Perfect powers in Horadam sequence

The Horadam sequence $\{W_n\}$ is defined by the Binet formula [Using notation from here]: $$W_n=\frac{A\alpha^n-B\beta^n}{\alpha-\beta}$$ where, $$A\ =\ b\ -\ a\beta \text{ and } B\ =\ b\ -a\alpha$$ $$\alpha = {p + d \over 2}, \beta = {p - d \over…
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Questions about the Conjecture $ X Y Z $

I really have a hard time asking this question. Because my mathematical background is almost at school level. I do not know in which theories of mathematics these questions are addressed. Unfortunately, since my English is insufficient, I will use…
lone student
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Found a formula for generating all numbers in all possibilities of all cycle lengths

yo, I'm about to spread some new knowledge about the collatz conjecture. Not sure if this has been shown before or not, but here: https://en.wikipedia.org/wiki/Collatz_conjecture#Cycles it states that all cycles up to 68 have been checked. Using my…
Cian Flint
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Does the infinite product of the reciprocals of a decreasing (or increasing) function equal zero?

I've made a short document explaining what I've just claimed. I'd like to know if the criteria for the infinite product to be zero is enough to hold for all decreasing and increasing functions. Theorem.
muhammad
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A conjecture of exercise type: $\gcd(a,b)^2=\gcd(a^2+b^2,ab)$

This must be known, but I haven't found it and want help to prove it: For all $a,b\in \mathbb Z$, $\gcd(a,b)^2=\gcd(a^2+b^2,ab)$ Tested for $10,000,000$ pseudo random number pairs. From time to time, when testing my growing math packages BigZ and…
Lehs
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Is there any approach proof for Legendre conjecture or it is completed solved?

Legendre conjecture stated that:for every x there exists a prime number between $x^2$ and $x^2+2x+1$ .then Is there any approach proof for legender conjecture or it is completed solved ?
zeraoulia rafik
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Repdigit Conjecture

I noted a conjecture down a while back after doing a fair few calculations on repdigits and noticing patterns. Define some digit repetition syntax for a 'string of integers' $x$ and an integer $y$, let $x;y$ be $x$ repeated and concatenated $y$…
Benedict W. J. Irwin
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Goldbach conjecture and primes

I need some clarification on (1) Is there any proof to say Mersenne primes $M_p$ are finite or infinite? if there, could you share here.. (2) If Goldbach is conjecture is true, how you can justify the statement" For all finite positive integer 2n…
vmrfdu123456
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Area of enclosed smooth curve is always irrational for rational dimensions

I have the intuition that smooth curves that are enclosed cannot be possible in real world , so it must be the case that either the dimensions(parameters) that define the curve ( like the radius of circle) are irrational or for real dimensions the…
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Can this heuristic on odd perfect numbers be made rigorous?

Can this heuristic on odd perfect numbers be made rigorous using the "Axiom of Choice"? Preliminaries Euler showed that an odd perfect number, if one exists, must take the form $N=q^k n^2$ where $q$ is prime with $q \equiv k \equiv 1 \pmod 4$ and…
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A conjecture on tensor product vectors

Consider a real vector space $V^{(1)}\otimes V^{(2)}$ where $\otimes$ is the tensor product. Product vectors are of the form $v_1\otimes v_2$ where $v_1\in V^{(1)}$, $v_2\in V^{(2)}$, anything else is a non-product vector. I conjecture the…
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Collatz Conjecture, sufficient to show odd numbers reach $1$?

The famous conjecture: Let $$ f(n) = \begin{cases} n/2 & \quad \text{if } n \text{ is even}\\ 3n+1 & \quad \text{if } n \text{ is odd}\\ \end{cases} $$ The Collatz Conjecture states that when applying this function repeatedly to any…
Carser
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Why proof by induction fails for Goldbach's conjecture?

Can anyone clarify why induction method fails for this conjecture?
john
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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 and functions already proved! Thanks to all the…
Andrea
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