Zimian问题与叙拉古算子方程初探

Research on Zimian Question and Syracuse Operator Equation

Zimian问题实质上是叙拉古算子方程 xi = S xi(xi >1)的解的存在性问题,Erd?s给出长度 m i =1 i = 1= 8的一组解.本文不仅给出了叙拉古算子方程有解的一个必要条件,指出了方程不存在长度 m = 1的解,还给出了方程在长度 m = 18, m = 13, = 10, = 8 和 m = 5 的若干组解.

Zimian question is essentially about the question of the existence of solution in Syracuse operator m m equation xi = S xi ( xi > 1). Erd?s gives a solution to Syracuse operator equation for m = 8. This paper not only i = 1 i= 1 gives a necessary condition of the solution existence about Syracuse operator equation, and proves the no-existence of solution in Syracuse operator equation for m =1,but also gives some solutions to equations for m = 8, m = 18, m = 13, m = 10, m = 5.