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- W3107410920 abstract "This self-contained communication summarizes, simplifies and extend some theorems we have previously demonstrated. If one of its main results is that at least almost all orbits of the Collatz map attain bounded values, the methodology of algebraic geometry it employs, that is, the studying of how the complete binary, ternary and quaternary trees intersect each other over N is its most important contribution as not only does it yield very useful results but also can it be applied to a large diversity of other cases of discrete mathematics and beyond. Defining S(a) = 2a + 1 and V (a) = 4a + 1 we first establish a founding lemma that for any even number x the orbits of V (x) and S(V (x)) merge and so do S k (V (x)) and S k+1 (V (x)) for any even k. For any odd number y the orbits of S(V (y)) and S 2 (V (x)) merge and so do S k (V (x)) and S k+1 (V (x)) for any odd k. An algorithm connecting all of those merging pairs with each other will therefore solve the Syracuse problem. We here demonstrate the existence of an algorithm finitely connecting at least almost all of these pairs all the way back to the pair {1;3}, along with a few corollaries that are worthy of interest to manifest a final proof of the Collatz conjecture." @default.
- W3107410920 created "2020-12-07" @default.
- W3107410920 creator A5080945099 @default.
- W3107410920 date "2020-02-22" @default.
- W3107410920 modified "2023-09-23" @default.
- W3107410920 title "At least almost all Collatz orbits attain bounded values." @default.
- W3107410920 hasPublicationYear "2020" @default.
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