| viXra.org > Number Theory > viXra:2504.0096 |
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| viXra.org > Number Theory > viXra:2504.0096 |
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Number Theory |
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Authors: Zhenghao Wu
We provide a general analytic formula to construct all existing starting odd numbers that obey our desired finite arbitrarily long Collatz trajectory, meaningthat these starting odd numbers obey our pre-designated maximum factors of 2 at each iteration of the reduced Collatz map. We also provide another generalanalytic formula for finding the resulting odd numbers after N iterations of the reduced Collatz map. These formulas shed light on the structure of Collatztrajectories and other properties. We can also use this information to find in finite steps all existing Collatz trajectories that become 1 after any finite N iterations.We also will see that the "location" of all of the 1’s in Collatz Conjecture can be found by solving a special case of the discrete log problem.
Comments: 21 Pages.
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[v1] 2025-04-15 21:55:34
[v2] 2025-04-18 01:19:02
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