The Kratz conjecture, also known as the 3N+1 conjecture, the odd-even unification conjecture, the Ullam problem, and the Kakutani conjecture, are known as the simplest unsolved mysteries in the history of mathematics.

How simple is it? It's so simple that even most elementary school students can understand it.

Take any positive integer, divide it by 2 if it's even, multiply it by 3 and add 1 if it's odd, and repeat the process until the result is 1.

This is the famous Kratz conjecture, and its simplicity makes it sound like a little game played by a teacher in math class for elementary school students.

However, it is precisely this mathematical problem, which can be said to be the simplest form of expression among the unsolved problems in the history of mathematics, that has plagued the mathematical community for nearly a hundred years.

Every year, a large number of mathematicians want to prove it, and although the world's top mathematicians believe it is correct, they can't prove it.

Intuitively, it may seem that the difference in the initial number will affect the final result, perhaps some numbers will start with 1, and start with other numbers and tend to infinity.

But this is not the case with Cratz's prediction, and he speculates that if the initial number is a positive whole and the process is repeated enough times, the final result will be 1, regardless of the initial number.

After that, 1 becomes the initial number and falls into a loop: 1, 4, 2, 1, 4, 2, 1

Let's say the number is 9, and then, here's how to do it:

9-28-14-7-22-11-34-17-52-26-13-40-20-10-5-16-8-4-2-1

Eventually, for all theoretical numbers, the sequence ends in a cycle of 4,2,1.

Xiao Ran looked at the Kratz conjecture proof formula in his mind, and could roughly see that the idea of solving the problem was a differential partial equation, but the specific steps and the application of some of the formulas involved were a little confusing.

I can only barely understand a small part of it by half-guessing and half-guessing.

"It seems that it will take a lot of time and effort to understand the formula for proving this Kratz conjecture." Xiao Ran exhaled deeply, and sighed inexplicably.

But even so, it didn't affect the excitement and excitement in his heart at all.

Although the Kratz conjecture is not as good as the seven conjectures in the millennial mathematical world, it is also a world-class mathematical conjecture, and its influence and fame are not much smaller.

Of course, this is also due to the fact that the Kratz conjecture is too simplistic compared to other world-class mathematical conjectures.

is completely a model of pretending to be a pig and eating a tiger, if the Riemann conjecture is compared to the Emperor of the Wild Sky who has been dictatorial for eternity in the online literature world, then the Kratz conjecture is undoubtedly the Yan Emperor Xiao Yan.

Either pretending to be a pig and eating a tiger or on the way to pretending to be a pig and eating a tiger, so every year it attracts a large number of mathematical talents to plunge into this bottomless giant pit one after another, and finally shed tears of regret in this infinite cycle of no hope.

If he published this Kratz conjecture, he didn't know if the whole world would be shocked, but the mathematical community would definitely tremble.

At that point, a Fields Medal is absolutely indispensable.

It can be said that at the moment when he held the Cratz conjecture in his hand, one of his hands had already touched the trophy of the Fields Medal, and it was up to him to publish it.

Thinking of this, he couldn't help rubbing his chin and fell into deep thought: "I don't know if solving the Kratz conjecture is enough to lift the ban on me Well, maybe it's a little unsafe, but a Fields Medal is definitely enough!" ”

You must know that there is only one winner in China who has won the Fields Medal, and that is Dean Qiu, who is now the dean of the Institute of Mathematics of Yan University.

One can imagine how high the gold content of the Fields Medal is.

Alas, although it is not to prove the Riemann conjecture, but to prove the Kratz conjecture is also so-so!

Hey!

"The next goal is to understand the Kratz conjecture, half a year, half a year is enough!"

"Go home and study!"

In the next two months, Xiao Ran basically belonged to the door and did not go out of the door, buried himself in study all day long, and lived an ascetic life.

In addition to going back to school halfway through to fill in the application form, I occasionally went to the library to borrow a few books.

By the way, I visited Lao Lu a few times, and let the old things explode at the same time.

easily abused Lao Lu and Lao Liu in more than a dozen games of chess, leaving a deep psychological shadow on the two old things.

Then there is about 8 o'clock in the evening of star fruit at the Golden Dragon Hotel to discuss life, in addition to in-depth and profound exchanges.

Then I occasionally went out to have a meal with Fang Qinya to warm up the relationship.

Well. If you look at it this way, in fact, the ascetics are not so bitter!

In addition, the foreign journal "Journal of Pure Mathematics and Applied Mathematics" also sent a message that the paper was successfully passed and can be published next month.

Time flies, and finally the day of school has come.

August 31, 8 a.m.

Modu Pudong Airport.

"Brother Xiao, here, here!" As soon as Xiao Ran stepped into the airport hall, Gu Ming in front of him waved his hand loudly regardless of the surprised eyes around him.

gave full play to his social cattle and second-hand attributes.

Next to Gu Ming, An Xin and Yang Xiaoxi were still standing, but at this moment, both of them blushed a little embarrassed because of Gu Ming's actions, and subconsciously moved a few steps away from him.

Not surprisingly, An Xin and Yang Xiaoxi were both admitted to Yan University, but An Xin chose to major in business administration, while Yang Xiaoxi, like Xiao Ran, chose to major in mathematics.

As for Gu Ming, Xiao Ran sighed secretly.

I can only sigh, bad fate!

This second goods college entrance examination scored 580 points, which is a few points away from the admission score line of Aurora University in the past.

Therefore, when school started, I happened to go to Yanjing with them.

"Stop shouting." Xiao Ran walked towards the three of them, and scolded Gu Ming angrily: "You don't want to be embarrassed, I'm still ashamed." ”

"Hehe, aren't you afraid that Brother Xiao didn't see it." Gu Ming squeezed his eyebrows and said, it is estimated that because of the start of school, this product is very excited at this time.

Xiao Ran didn't bother to pay attention to these two goods, turned his gaze, put his eyes on An Xin and Yang Xiaoxi, and said hello: "An Xin, Xiaoxi." ”

"Xiao Ran, good morning." Yang Xiaoxi whispered shyly, looked at Xiao Ran, and immediately lowered his head in a panic and buried his head in the heavy fruit.

An Xin was already accustomed to the performance of her table mates and girlfriends, and nodded calmly: "Just waiting for you, there is still half an hour to board the plane, let's go get the boarding pass first." ”

Half an hour later, four people lined up to follow the flow of people to board the plane one after another.

"Sir, you are welcome to take this flight, may I ask what number of seat is you?" As soon as Xiao Ran entered the cabin, the beautiful stewardess standing at the door asked with a smile.

said to be a beauty, in fact, it should be said that it is a beautiful stewardess, who looks about thirty years old, with a mature and elegant face, long black hair coiled up at the back of her head, and a royal blue stewardess uniform wrapped around her slender body is particularly gorgeous and moving.

Xiao Ran glanced at the sign on the chest of the beautiful flight attendant, Yu Manli.

Glancing at the boarding pass again, he said to Manli: "F class, 4C, thank you." ”

Yu Manli smiled professionally and said to Xiao Ran: "Sir, please." ”

After speaking, he took the first step to lead Xiao Ran to the cabin, twisting and twisting his big buttocks, which made Gu Ming, who was following Xiao Ran, blush.

I want to pretend to be serious and not squint ahead, but I can't hold back a turbulent heart in adolescence, and I can't stop peeking somewhere, and I'm afraid of being discovered by others, so I immediately shift my gaze after peeking at it, and within two seconds, my eyes returned to the original place.

It can only be said that the water and soil at the airport are to raise people, and as soon as he entered the plane, he almost cured Gu Ming's myopia for many years.

Soon, the stewardess took the two of them to the corresponding seats and said softly: "Please take a seat, I'll help you put your luggage, right?" As he spoke, he wanted to pick up Xiao Ran's luggage.

Xiao Ran stopped her movements and said with a smile: "No need, I'll do it myself!" ”

The stewardess smiled and nodded: "Then if you need anything, please just tell me, just press this button." He gestured to a green button next to a chair.

Gu Ming opened his mouth, as if he wanted to open his mouth to say something, but in the end he closed his mouth depressedly and put his luggage away in a sullen manner.

After the flight attendant left, he glanced at Xiao Ran with some resentment: "Brother Xiao, am I so non-existent?"

"What do you mean by that?" Xiao Ran asked half-lying on the big chair in the first-class cabin without raising his eyelids.

"Why is that stewardess so attentive to you from beginning to end, treating me like she can't see me!!" Gu Ming gritted his teeth, his eyes were red with envy and jealousy.

"Oh, you said that." Xiao Ran picked up a magazine and put it on his face, and said in a calm tone.

"I've been on this flight several times before."

"That's it?"

"Well, by the way, I communicated with her in private."

Gu Ming:.

"It's moist!" Xiao Ran added.

Gu Ming: !!

"Brother Xiao, you really deserve to die!!!"

After the plane flew for about half an hour, the flight attendants began to distribute in-flight meals and drinks to the passengers, Yu Manli came to Xiao Ran and asked softly: "Mr. Xiao, may I ask, do you need to drink?" We have black tea, coffee, fresh milk, and freshly squeezed juices. ”

Xiao Ran removed the magazine on her face and opened her eyes, only to see Yu Manli's bright and bright eyes with heavy makeup looking at her, noticing Xiao Ran's eyes, the corners of her eyes were slightly raised, and her eyes were shining, with a hint of seductive smile.

"Bring me a cup of coffee."

"Okay." Yu Manli responded, and her expression suddenly became lost.

"Mr. Gu, what do you want to drink?" With a reluctant smile on her face, she asked Gu Ming next to her again.

Have you finally noticed my presence?

Gu Ming burst into tears, "Give me a glass of milk!" ”

"Okay, okay!" Yu Manli's expression froze obviously, but she instantly returned to normal and poured him a glass of milk.

Looking at Yu Manli's distant back, Gu Ming looked at Xiao Ran with some puzzlement: "Why did her expression seem to be something wrong when I said I wanted milk?" ”

Xiao Ran said lightly: "Because that's my code with her." ”

"What code?" Gu Ming asked innocently.

Xiao Ran: "The code to go to the toilet." ”

Gu Ming:.

I can't sit on this broken plane!!

Xiao Ran looked at Gu Ming, who had broken the defense, speechlessly, and could only roll his eyes and ignore this guy anymore.

Until the plane was about to start landing, and the flight attendants began to pack up the water cups on the small table in front of the passengers, Yu Manli came to Xiao Ran's side again, and handed him a small note without a trace when she put away his water glass.

Xiao Ran smiled slightly, put away the note, and after she walked away, she casually stuffed it into the bag on the backrest.

When he got off the plane, the crew members were standing at the door to see off the passengers, and when Xiao Ran left, he saw that among the crew members, Yu Manli smiled and said goodbye to him, and glanced at him sultryly.

Xiao Ran smiled faintly, raised his hand, and got off the plane without looking back.

Gu Ming, who was following behind Xiao Ran, saw this scene, and he was completely numb.

What is the number of the airline?

I can't stand it anymore! I'll fly this airline again in the future, I'm a dog!

Thank you for the 1000 points reward from the big guy, and thank you for the support of the big guy!

(End of chapter)