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- W4382491410 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." @default.
- W4382491410 created "2023-06-29" @default.
- W4382491410 creator A5090478768 @default.
- W4382491410 date "2023-06-27" @default.
- W4382491410 modified "2023-09-26" @default.
- W4382491410 title "Are the Collatz and abc conjectures related?" @default.
- W4382491410 doi "https://doi.org/10.48550/arxiv.2306.15284" @default.
- W4382491410 hasPublicationYear "2023" @default.
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