This question was put forward in the 1950s. In the west, it is often called Syracuse conjecture, because it is said that this problem was first studied at Syracuse University in the United States. In the East, this problem is named after Kakuguchi, a Japanese mathematician who brought it to Japan, and is called the Corner-Valley Conjecture. Besides, it has many other names, which are probably related to mathematicians or places that study and spread it: Klaz problem, Hasselblad algorithm problem, ulam problem and so on. Today, in mathematical literature, people simply call it 3x+ 1 problem.

When talking about the history of this conjecture, Kakuguchi said: In a month's time, everyone at Yale University devoted themselves to solving this problem, but there was no result. The same thing seems to have happened at the University of Chicago. Some people suspect that this problem is a conspiracy of the Soviet KGB to hinder the development of mathematics in the United States. But I doubt whether the KGB has such a broad vision of mathematics. This form is so simple, but so difficult to solve, it is really difficult to meet.

Mathematicians have published many serious papers on number theory in 3x+ 1, and discussed this problem from all aspects. I will introduce these developments later. However, the problem itself has never been solved. We don't know whether we will get 1 all the time.

1996, B. Thwaites offered a reward 1 100 to solve this problem. I wrote down this document offering rewards: thwaites, B. Two agreements, or how to win-100. math. gaz. 80, 35-36, 1996, so that in case the certificate comes out, everyone will know where to receive the prize. For Uncle Qian's sake, the 3x+ 1 problem also has a name, called Thwaites conjecture.

If there is such a natural number, and we do the above transformation repeatedly, we will never get 1, then there are only two possible situations.

1) falls into another cycle different from 4→2→ 1. Later, we can see that if this happens, then the number in such a cycle and the length of this cycle will be very huge;

2) There is no loop. In other words, the result of each transformation is different from all the results obtained before. In this way, we will get more and more results (of course, there may be a temporary reduction, but the general trend is that the results tend to infinity).

The programming of 3x+ 1 problem algorithm in C language is actually very simple, and beginners in C language can understand it:

# include & ltstdio.h & gt

Long trunk line ()

{

Long x, I, t;

Printf (input x:);

scanf(%d，& ampx)；

do

{

if(x%2==0)

I = x/2；

other

I = 3 * x+ 1；

printf(%d，I)；

x = I；

}

And (x! = 1);

Returns 0;

}

As shown in the figure, the execution result is 1 million: