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This paper presents a preliminary mathematical investigation of the Collatz conjecture. It derives an identity for iterates of an accelerated odd-only map, establishes a necessary condition for cycles, examines the possibility of a two-element cycle, and considers restrictions on a hypothetical smallest counterexample. The results are partial and do not constitute a proof of the Collatz conjecture.
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Auelkhan Yerassyl (2026) studied this question.
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