One potential counterexample of the Collatz conjecture would be if there was a number that looped back to itself. Of course, this would still not prove the conjecture because some sequences could still potentially diverge to infinity. Has it been proven that Collatz sequences cannot repeat?
2026-03-29 01:33:58.1774748038
Can it be proven that Collatz numbers cannot repeat?
1.2k Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in NUMBER-THEORY
- Maximum number of guaranteed coins to get in a "30 coins in 3 boxes" puzzle
- Interesting number theoretical game
- Show that $(x,y,z)$ is a primitive Pythagorean triple then either $x$ or $y$ is divisible by $3$.
- About polynomial value being perfect power.
- Name of Theorem for Coloring of $\{1, \dots, n\}$
- Reciprocal-totient function, in term of the totient function?
- What is the smallest integer $N>2$, such that $x^5+y^5 = N$ has a rational solution?
- Integer from base 10 to base 2
- How do I show that any natural number of this expression is a natural linear combination?
- Counting the number of solutions of the congruence $x^k\equiv h$ (mod q)
Related Questions in COLLATZ-CONJECTURE
- Why do these Collatz values seemingly explode and then implode?
- What's the image of the function $f(x)=(3x+2^{v_2(x)})$ on the Prufer 2-group?
- Assuring Lipschitzian and contraction of a mapping
- Finding an equation for fixed points
- Are there any false variants of the Collatz conjecture for which the probability heuristic works?
- Investigating natural numbers in relations with prime numbers
- Some details about 'Collatz Conjecture'?
- Are the prime-free sequences $x_{n+1}=4x_n+1$ of odd numbers in bijection with the square numbers greater than $16$?
- Simplistic Odd Collatz formulas
- Are there specific numbers for which the Collatz Conjecture is proven?
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?
No but it has been proven that if a cycle exist it is large and has certain properties.
Simons & de Weger (2003) extended this proof up to 68-cycles: there is no k-cycle up to k = 68.[13] Beyond 68, this method gives upper bounds for the elements in such a cycle: for example, if there is a 75-cycle, then at least one element of the cycle is less than 2385×2^50... from collatz wiki
from the connection between cycle length and maximum number in cycle they can be exaustivly searched and cycle of that length disproven. but no general result.