The Structure of the 3x + 1 Function: An Introduction (original) (raw)

The 3x+1 problem: An annotated bibliography (1963--1999)

Jeffrey Lagarias

2003

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The 3x+ 1 Problem: An Annotated Bibliography, II (2000-2009)

Jeffrey Lagarias

Arxiv preprint math/0608208, 2006

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Some Observations on the 3x+1 Problem

Dhananjay Mehendale

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The 3x+ 1 problem: An annotated bibliography (1963--1999)(sorted by author)

Jeffrey Lagarias

Arxiv preprint math/0309224, 2003

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The 3 x + 1 Problem : An Annotated Bibliography ( 1963 – 2000 )

Jeffrey Lagarias

2006

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3x + 1 Problem Annotated Bibliography

Jeffrey Lagarias

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Is a solution to the 3x + 1 problem in sight?

Peter Schorer

SIGACT news, 1997

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The 3x+1 Problem: An Overview

Jeffrey Lagarias

Cornell University - arXiv, 2021

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On the 3x+1 conjecture

Peter Hellekalek

arXiv (Cornell University), 2016

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A Binomial Representation of the 3x + 1 problem

Yuri Matiyasevich, Maurice Margenstern

ACTA ARITHMETICA-WARSZAWA-, 1999

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The proof of 3x+1 problem

IOSR Journals

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The 3x+1 Problem as a String Rewriting System

Joseph Sinyor

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3n+1 Problem and its Dynamics

Bishnu Hari Subedi

Nepal Journal of Mathematical Sciences

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A new inherent approach to solving the Collatz 3n+1 problem and its analogues

Mikhail Bokiy

Preprint, 2025

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Density bounds for the 3x+13x+13x+1 problem. I. Tree-search method

Jeffrey Lagarias

Mathematics of Computation, 1995

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Bounds for the 3x+1 problem using difference inequalities

Ilia Krasikov

Acta Arithmetica, 2003

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The algorithmic structure of the finite stopping time behavior of the 3x + 1 function

Mike Winkler, Ph.D.

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The Collatz Problem: The Demonstration

Junior Mukomene

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New lower bounds for the size of a non-trivial loop in the Collatz 3x+ 1 and generalized px+ q problem

Roupam Ghosh

Arxiv preprint arXiv:0907.3086, 2009

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Proving and Proof of 3n + 1 or Collatz Conjecture: The Traps, an Analysis and a Flowchart and Their ID (Identification

Ismael T Fortunado

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One Way Function Candidate based on the Collatz Problem

Rade Vuckovac

ArXiv, 2018

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About the combination of: harmonic intervals built on the 'tetrada', the problem 3x+1 and the fundamental constant 4:3

Эдуард Дяченко

2020

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ON THE GRAPH REPRESENTATION OF THE 3n + 1 CONJECTURE

Fidan Nurİyeva

2024

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Solution to the Collatz Conjecture

Samuel Ferrer Colás

Solution to the Collatz Conjecture

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A Solution to the 3x + 1 Problem

Peter Schorer

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Some natural generalizations of the Collatz Problem

Walter Carnielli

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On the Collatz Problem

Roupam Ghosh

Arxiv preprint arXiv:0804.3716, 2008

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The 3x + 1 semigroup

Jeffrey Lagarias

2005

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A dynamical approach towards Collatz conjecture

Pablo Castaneda

arXiv: Dynamical Systems, 2019

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The 3x+1 problem: An annotated bibliography

Jeffrey Lagarias

2003

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Existence of repetitions of digits in the construction of periodic sequences related to 3x+1 problem Proof of the theorem on the periods in the 3-adic representation of terms of periodic sequences that appear in Collatz problem

yagub aliyev

2016 IEEE 10th International Conference on Application of Information and Communication Technologies (AICT), Baku, Azerbaijan, 12-14 Oct. , 337-340. , 2016

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A Simple binary analysis of the Collatz Conjecture

Daniele Grosso

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The Collatz tree as a Hilbert hotel: a proof of the 3x + 1 conjecture

Jan Kleinnijenhuis

2021

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Kiran-S-1-Kedlaya The William Lowell Putnam Mathematical Com

Muhammad Andyk Maulana

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A note on the Diophantine equation 𝑥ⁿ+𝑦ⁿ+𝑧ⁿ=3

Abraham Boyarsky

Mathematics of Computation, 1984

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