Open Access3n+1 Problem and its Dynamics
Author(s) -
Bishnu Hari Subedi,
Ajaya Kumar Singh
Publication year - 2020
Publication title -
nepal journal of mathematical sciences
Language(s) - English
Resource type - Journals
eISSN - 2738-9928
pISSN - 2738-9812
DOI - 10.3126/njmathsci.v1i0.34159
Subject(s) - collatz conjecture , conjecture , mathematics , integer (computer science) , generalization , number theory , combinatorics , holomorphic function , function (biology) , discrete mathematics , pure mathematics , computer science , mathematical analysis , evolutionary biology , biology , programming language
The subject of this paper is the well-known 3n + 1 problem of elementary number theory. This problem concerns with the behaviour of the iteration of a function which takes odd integers n to 3n + 1, and even integers n to n/2. There is a famous Collatz conjecture associated to this problem which asserts that, starting from any positive integer n, repeated iteration of the function eventually produces the value. We briefly discuss some basic facts and results of 3n + 1 problem and Collatz conjecture. Basically, we more concentrate on the generalization of this problem and conjecture to holomorphic dynamics.