English

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.

Keywords

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

R2 v1 2026-06-23T09:14:39.856Z