English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

The Collatz Conjecture (also known as the 3x+1 Problem) proposes that thefollowing algorithm will, after a certain number of iterations, always yieldthe number 1: given a natural number, multiply by three and add one if thenumber is odd, halve the resulting number, then repeat. In this article, foreach $N$ for which the Collatz Conjecture holds we define the $N^{th}$ Collatzpolynomial to be the monic polynomial with constant term $N$ and $k^{th}$ term(for $k > 1$) the $k^{th}$ iterate of $N$ under the Collatz function. Inparticular, we bound the moduli of the roots of these polynomials, provetheorems on when they have rational integer roots, and suggest furtherapplications and avenues of research.

Collatz polynomials: an introduction with bounds on their zeros