论文标题
Collatz猜想：通过结构化方法的博览会和证明
Collatz Conjecture: Exposition and Proof Through A Structured Approach
论文作者
论文摘要
Collatz猜想的结构化方法仅使用奇怪的整数依次根据其扮演的角色（例如起动器，中间和终端）分为类别。表达式4x+1被用作一种工具，以揭示导致我们证明其证明的猜想的所有隐藏和重要特征。迭代材料的混合特性是通过表明表格4m+3的所有奇数整数中一半的collatz迭代来解决的，平均而言，迭代的迭代率是奇数整数的值的三倍，而奇数整数的值则是始于4m+1的迭代物的迭代物，而平均为4m+1的迭代率。此外，还提供了表达式来生成所有奇数集的集合，其中每个整体中所有整数的collatz迭代是形式6m+1或6m+5的整数。 Collatz Net（树）的意义变得显而易见，因为它涵盖了所有Collatz轨迹。
A structured approach for the Collatz conjecture is presented using just the odd integers that are, in turn, divided into categories based on the roles they play such as Starter, Intermediary and Terminal. The expression 4x+1 is used as a tool to expose all the hidden and significant characteristics of the conjecture that lead us to its proof. The mixing properties of the iterates are addressed by showing that the Collatz iterates of half of all the odd integers that are of the form 4m+3, on the average, increase by three times the value of the odd integer that was used to start with, while the iterates of those of 4m+1, on the average, decrease by a factor of four. Further, expressions are provided to generate all the sets of odd integers where the Collatz iterate of all the integers in each set is an integer of the of form 6m+1 or 6m+5. The significance of the Collatz net (tree) becomes obvious since it encompasses all the Collatz trajectories.
