Year: 2025
Type: article
Abstract: The Collatz and abc conjectures, both well known and thoroughly studied, appear to be largely unrelated at first sight. We show that assuming the abc conjecture true is helpful to improve the lower bound of integers initiating a particular type of Collatz sequences, namely finite sequences of a given length where all terms but one are odd with the usual “shortcut” form. To obtain sharper bounds in this context, we are led to consider a small subset of the abc-hits. Then, it turns out that Collatz iterations as well as Wieferich primes may be used to find large triples in this subset.
Source: Experimental Mathematics
Author: Olivier Rozier
Institutions: Institut de physique du globe de Paris, Université Paris Cité
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4382299857