On Collatz Conjecture for binary polynomials

TL;DR

This paper introduces a polynomial variant of the Collatz Conjecture over the finite field _2 and provides a proof that this variant is resolved, including multiple illustrative examples.

Contribution

The paper formulates and proves a Collatz-like conjecture for polynomials over _2, a novel extension of the classical problem.

Findings

The polynomial Collatz variant is proven to be solved.

Several examples illustrate the behavior of the polynomial Collatz process.

Abstract

We build a variant of Collatz Conjecture for polynomials over $\mathbb{F}_2$ and we prove that it is solved. By the way, we give several examples.