Number Theory

    

Nuanced Truth of Collatz Conjecture

Authors: Pierre Lamothe

The algebra of transition functions between elements of generalized Collatz sequences has revealed the true nature of cycles. The structure of the cyclic invariant enables us to demonstrate both:
a) The Syracuse conjecture cannot be substantiated as absolute veracity because no matter the length, a random cycle is theoretically possible.
b) The Syracuse conjecture can only hold true in practice with exceedingly probable status due to the exponential decay of a cycle’s probability as a function of length.

Comments: 15 Pages. In French

Download: PDF

Submission history

[v1] 2023-10-24 01:22:55
[v2] 2023-10-30 21:07:58

Unique-IP document downloads: 186 times

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