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arXiv · 2601.17573

Weakly and Strongly Admissible Triplets for a Collatz-Type Map

Abderrahman Bouhamidi
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Abstract

In this paper, we investigate a class of Collatz-like problems associated with weakly and strongly admissible triplets of integers. This framework extends the classical Collatz mapping, providing a systematic method for generating triplets with convergence to cycles, thereby bypassing the difficulties inherent in solving Diophantine equations. We introduce several special families of admissible triplets and establish general structural properties. In addition, we propose conjectures that generalize the classical Collatz conjecture. Bounds on the lengths of potential non-trivial cycles are derived and analyzed, and two algorithms are presented for computing lower bounds on cycle lengths. Finally, experimental tests are given to illustrate our approach.

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Abderrahman Bouhamidi. 2026-01-24. Weakly and Strongly Admissible Triplets for a Collatz-Type Map. https://arxiv.org/abs/2601.17573

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