A polynomial approach to the Collatz conjecture
Number Theory
2019-05-22 v1 Symbolic Computation
Abstract
The Collatz conjecture is explored using polynomials based on a binary numeral system. It is shown that the degree of the polynomials, on average, decreases after a finite number of steps of the Collatz operation, which provides a weak proof of the conjecture by using induction with respect to the degree of the polynomials.
Cite
@article{arxiv.1905.08462,
title = {A polynomial approach to the Collatz conjecture},
author = {Feng Pan and Jerry P. Draayer},
journal= {arXiv preprint arXiv:1905.08462},
year = {2019}
}
Comments
7.5 pages and 1 Figure