A Solution to the Collatz Conjecture Problem

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Abstract

Research Collatz odd sequence, change (×3 + 1) ÷ 2k operation in Collatz Conjecture to (×3 + 2m − 1) ÷ 2k operation. Expand loop Collatz odd sequence (if exists) in (×3 + 2m − 1) ÷ 2k odd sequence to become ∞-steps non-loop sequence. Build a (×3 + 2m − 1) ÷ 2k odd tree model and transform position model for odds in tree. Via comparing actual and virtual positions, prove if a (×3 + 2m − 1) ÷ 2k odd sequence can not converge after ∞ steps of (×3 + 2m − 1) ÷ 2k operation, the sequence must walk out of the right boundary of the tree.

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