Number Theory

    

Convergence and Divergence Analysis of the Qx+r Problem

Authors: Song Li

This paper investigates the convergence and divergence of the $qx+r$ problem (Crandall conjecture), which is a generalization of the $3x+1$ problem (Collatz conjecture). Through probabilistic analysis, we establish that the convergence condition for the $qx+r$ problem is $q<4$,and predict that it converges to the precise value $frac{r}{4 - q}$ ; when $q>4$, the transformation sequence diverges to infinity. The results of this study provide new insights into understanding the dynamic behavior of the $qx+r$ problem.

Comments: 4 Pages.

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[v1] 2025-03-11 21:10:41

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