Results 21 to 30 of about 141 (103)

Proof of the Collatz Conjecture

, 2023
Take any positive integer N. If it is odd, multiply it by three and add one. If it is even, divide it by two. Repeatedly do the same operations to the results, forming a sequence. It is found that, whatever the initial number we choose, the sequence will eventually descend and reach number 1, where it enters a closed loop of 1- 4 - 2 - 1. This is known
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Statistical Analysis of Descending Open Cycles of Collatz Function

Mathematics, 2023
Collatz dynamic systems present a statistical space that can be studied rigorously. In a previous study, the author presented Collatz space in a unique dynamic numerical mode by tabulating a sequential correlation pattern of division by 2 of Collatz ...
Kamal Barghout, Wadii Hajji, Nidal Abu-Libdeh, Mohammad Al-Jamal   +3 more
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Collatz Conjecture - The Proof

, 2023
In this paper, we prove the Collatz conjecture. We show that if a given number can be represented in a form of a certain specific equation then Collatz conjecture is true for that particular number. Next we propose a procedure that for a given number produces this specific equation and we prove that for every initial positive integer, such equation can
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Boolean Hypercubes, Mersenne Numbers, and the Collatz Conjecture

Journal of Mathematical Sciences and Modelling, 2020
This study is based on the trivial transcription of the vertices of a Boolean \textit{N}-Dimensional Hypercube $\textbf{H}_{N} $ into a subset $\mathbb{S}_{N}$ of the decimal natural numbers $\mathbb{N}.$ Such straightforward mathematical manipulation ...
Ramon Carbó Dorca
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Conjectures analogous to the Collatz conjecture [PDF]

Open Communications in Nonlinear Mathematical Physics
In this paper we introduce some conjectures analogous to the well-known Collatz conjecture.
Fabio Briscese, Francesco Calogero
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A Proof of Collatz Conjecture

, 2023
In 1937,German mathematician L.Collatz proposed the following conjeture:for any positive integer,if it is even,divide it by 2,if it is odd,multiply it by 3 and add 1 to get an even number.Continuing with the above rule, the final result will be 1.This paper gives a proof of this conjecture.
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Collatz Attractors Are Space-Filling

Mathematics, 2022
The algebraic topology of Collatz attractors (or “Collatz Feathers”) remains very poorly understood. In particular, when pushed to infinity, is their set of branches discrete or continuous? Here, we introduce a fundamental theorem proving that the latter
Idriss J. Aberkane
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A New Approach on Proving Collatz Conjecture

Journal of Mathematics, 2019
Collatz Conjecture (3x+1 problem) states any natural number x will return to 1 after 3⁎x+1 computation (when x is odd) and x/2 computation (when x is even). In this paper, we propose a new approach for possibly proving Collatz Conjecture (CC). We propose
Wei Ren
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On Collatz conjecture

, 2023
Different aspects of the Collatz Conjecture are discussed using representation of a positive integer n via terms of its Collatz sequence (k_i): n= (k_i×2^i-b_i )/3^(c_i ) .
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On local semirings induced by topologies: An algebraic approach to the Collatz conjecture

Applied General Topology
We present an algebraic approach to the Collatz conjecture by studying the topology τf  on ℕ induced by the Collatz function f, where the open sets θ ⊂ ℕ satisfy f-1 ( θ ) ⊂ θ .
Angel Guale, Jorge Vielma
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