Sitting in the VIP room of the airport's departure hall, Qin Ke sat on the sofa and wrote calculations. Qin Xiaoke pulled Ning Qingyun around the VIP room curiously, and assistant Fang Yongtang talked with the flight attendant next to him.

The staff communicated about baggage check-in.

This time the four of them were going to Jizhou to visit Academician Wang Heng. They bought a lot of gifts and had to take a high-speed train after getting off the plane. Assistant Fang was responsible for following up on these travel matters.

Fang Yongtang has been working with Qin Ke and Ning Qingyun for more than a year. As an assistant to these two small bosses, he doesn't have to be angry or worry about the unwritten rules of the workplace. Moreover, Qin Ke and the two treat the people around them very well, and their salary and remuneration are even better.

I don’t know how many former classmates, colleagues and friends expressed real envy after hearing about Fang Yongtang’s work.

Recently, the blind dates introduced to her by her family have changed from urban white-collar workers to high-quality men with higher social status, such as company executives and university faculty.

Fang Yongtang's eyes have also become picky. Although she is almost thirty, she is an "elderly leftover girl" in the eyes of everyone, and she is not very beautiful, but so what? Now she can learn to recharge her batteries after work.

Her social status is also high. Every time she comes to communicate on behalf of two small bosses, who doesn't give her some face?

And she is used to the "superpowers" and true temperament of the two small bosses. She looks down on the so-called "elites" who are well-dressed. She even thinks that it is not bad to be single like this. Who says that women must get married?

Generally speaking, Assistant Fang is very satisfied with her job. If she could, she would be happy to follow two small bosses in her life. Therefore, she usually works very conscientiously and helps everyone with everything, whether it is life or company matters.

Qin Ke and Ning Qingyun greatly relieved the burden.

Of course, there is also a problem with working for these two small bosses, that is, because the work is so comfortable, her face becomes round.

"The Rebirth of Financial Giants"

Unlike Assistant Fang, who is mature and temperamental and interacts with others with a smile, Qin Xiaoke, who is only fifteen years old, is obviously much more cheerful and lively.

For Qin Xiaoke, this trip to Jizhou is a long trip, so she is very excited.

Moreover, this was her first time flying in a first-class cabin, and she was full of expectations.

Before, she and Qin Ke only took business class from Yuanzhou to Beijing. This time it was because the business class had no tickets. Qin Ke was reluctant to let the two girls squeeze into the economy class. Anyway, he was not short of money now.

With a wave of his hand, he asked his assistant Fang Yongtang to buy four first-class tickets.

Qin Ke ignored the chirping of the little girl in the VIP waiting room. He had nothing to do and resumed research on the hail conjecture that had been suspended for ten days.

After all, it is impossible for him to deal with matters related to EDA issues in public.

The hail conjecture is indeed a very interesting topic. No matter which natural number it is, if it is an odd number, multiply it by 3 and add 1; if it becomes an even number, divide it by 2; how to calculate it repeatedly, no matter the numerical value changes in the process

No matter how big it is, it will eventually fall inexorably and quickly like hailstones, turning into the three numbers 4-2-1 that cycle endlessly.

Qin Ke is currently studying the special value 27.

The special thing about 27 is that its rise and fall far exceed the other values ​​within 100. Qin Ke has seen it in a certain document before, saying that 27 needs to go through 77 steps of transformation before it reaches the peak range.

9232, and after another 34 steps, it finally fell to the bottom value of 1.

That’s a total of 111 steps!

As for the odd number 23, which is similar to 27, the entire process only requires 16 steps, which shows how special 27 is.

Because of the specialness of 27, many mathematicians have tried to use 27 as a breakthrough point to solve the hail conjecture, and have basically come to the conclusion that this is a key branch point of a hail tree.

Therefore, the key point of branching refers to the part of the natural numbers branched out from here, which has an independent and powerful "hail effect".

For example, if 27 is used as the key branch point,... there will be a relatively long hail distance, and the "hail effect" exceeds that of nearby numbers.

Qin Ke can complete the entire rising and falling process of 27 using mental arithmetic in his mind. He mainly calculates how many similar branching key points there are, hoping to discover common patterns. Unfortunately, the larger the subsequent calculations, the greater the amount. Qin Ke temporarily

I couldn't find any useful rules.

It is worthy of being ranked among the top 100 mathematical problems in the world. No wonder some people call it "the next Fermat conjecture". It is also no wonder that Professor Tao, known as "the genius among mathematical geniuses", once lamented: "The 3N 1 problem is in 2

It cannot be proven by any current mathematical method within ten years."

Although Professor Tao said something similar to giving up, in fact, he is the only world-renowned mathematician who has given a probability proof of the hail conjecture - "Suppose f is a function whose domain is an integer and when n tends to infinity, f

(n) tends to infinity, then for almost all n, the minimum value in the 3n 1 sequence starting from n is less than f(n)".

This is currently the most important result in the hail conjecture.

Finding that the draft in his hand was full, Qin Ke stopped writing and shook his aching wrist.

Today's attack on the Hailstorm conjecture is still in vain.

Similar situations have occurred countless times.

To this day, he and Ning Qingyun are still in the stage of looking for proof ideas, but Qin Ke is not discouraged. Didn’t it take more than half a year to figure out the Polignac conjecture? Now he has studied the four hailstone conjectures.

There may not be any big breakthroughs in a few months. As long as you continue to accumulate experience and judge which roads are not feasible, you will always find the most correct road.

After putting away the draft, Qin Ke casually picked up the magazines on the magazine rack and flipped through them. These magazines were basically about travel and fashion, and he had little interest in them.

Picking up the coffee and taking a sip, I heard Qin Xiaoke and Ning Qingyun next to me discussing an old movie "The Butterfly Effect". God knows how their conversation got to this point.

This chapter is not finished yet, please click on the next page to continue reading the exciting content! "Sister Ning, do you think you can really travel through time and go back to the past? My brother also said before that because of some 'space-time paradox', talking about people

It is impossible to go back to the past of the same world, unless it is the past of another parallel world, which has no intersection with the current world and cannot affect this world."

Ning Qingyun was particularly patient with Qin Xiaoke. She said warmly: "Yes, from the perspective of quantum physics, parallel worlds explain the existence of 'Schrödinger's cat' in two states: 'cat alive' and 'cat dead' at the same time."

It is a self-consistent statement that can also ensure that the Schrödinger equation can be established and the wave function does not collapse. Therefore, the 'Butterfly Effect' is actually a story of traveling through different parallel worlds. Every change jumps out of the original timeline and enters a new one.

parallel world."

Qin Xiaoke had a confused look on his face: "Sister Ning, you speak just like my brother. I can't quite understand you, but I think it's very powerful. You two are a match made in heaven. Well, hello, sister-in-law."

Ning Qingyun's face was hot, especially the words "Hello, sister-in-law" always reminded her that Xiaoke actually knew that she and Qin Ke had had a very close relationship. She saw Qin Ke next to her smiling at her.

She winked, blushed, and went over to pinch his waist gently: "Xiao Ke also asked about whether the 'butterfly effect' in that movie will definitely appear. You can answer it for her."

Qin Ke enjoyed the little intimate play with Ning Qingyun. He held the girl's soft little hand, pulled her to sit next to him, and waved to Qin Xiaoke, waiting for the little girl to approach.

smiled and said:

"The 'Butterfly Effect' is a word that belongs to chaos theory. It uses an abstract concept to describe, that is: very small changes in initial conditions, if continuously amplified, will cause extremely huge differences in its future state. It belongs to right and wrong.

The inherent characteristics of linear dynamic systems are a common phenomenon in nonlinear systems..."

When Qin Ke said this, he suddenly remembered that there is a typical example in mathematics to illustrate the butterfly effect, which is the "cotangent sequence".

For example, 1, 1.00001, and 1.0001 continuously make cotangents. At the beginning, the cotangent values ​​are very close, but after the 10th term, the differences between the three series have become huge. In other words, after enough times, the cotangent values ​​​​are very close.

After cotangent, the final numerical value can be regarded as completely random and chaotic.

What started as such a small difference turned out to be completely different... Hey, isn't this exactly the opposite of the "hail conjecture"?

In the hail conjecture, no matter how big the difference is in the natural numbers at the beginning, such as 2 and 100 million, they will eventually fall to 1, that is, no matter how big the difference is in the beginning, the results will tend to be the same.

Obviously both the "cotangent sequence" and the "hail conjecture" are based on clear mathematical rules, but the results are completely opposite. One result is random, and the other is fixed. Why is there such a big difference?

An idea flashed across Qin Ke's mind.

By the way, can we find an idea to prove the hail conjecture by delving into the reverse derivation of the "cotangent sequence"?

Qin Ke fell into deep thought.

Qin Xiaoke said strangely: "Brother, why did you just..." in the middle of your sentence?

Ning Qingyun hurriedly grabbed her: "Xiao Ke, don't disturb your brother, he seems to have thought of something important."

Qin Ke thought for nearly ten minutes before taking out a new draft book and started counting.

"The cotangent sequence can be regarded as countless observations of a continuous random variable X, which can be described by a distribution function:"

"F(x)=1/2 1/πar(x/a),,..."

Qin Ke wrote faster and faster, until the boarding beep sounded repeatedly, and he reluctantly stopped writing.

He was about 60% sure that this idea would work.

Yes, through the research on the "cotangent sequence" just now, Qin Ke came up with an idea, which is to try to visualize the graphics of different natural numbers. The range of each natural number is fixed and has a corresponding value. As long as

By converting it into two-dimensional coordinates, it is possible to use the mathematical method system of "Ling Lemon Number Theory Hypergeometric Mapping Method" to solve it.

Of course, this is only a possibility, and it will be a long and arduous task to study the visual pattern patterns of different natural numbers and different ranges.

But this is the biggest gain recently. At least there is a more likely direction. The rest will be slowly studied and refined with Ning Qingyun.

Qin Ke stretched, stood up and smiled at Ning Qingyun and Qin Xiaoke: "Let's go, let's board the plane."

…

Jizhou is a famous historical city with many cultural attractions.

Qin Ke and Ning Qingyun took Qin Xiaoke to visit the scenic spots in the morning, and in the afternoon and evening they chatted with the old academician Wang Heng, teaching him the "Oriental Peiyuan Method" and listening to his mathematics teachings.

Academician Wang Heng is indeed the leading number theory master in the country. Now that he, Qin Ke and Ning Qingyun have the status of teacher and student, he naturally gives careful guidance to them.

Qin Ke and Ning Qingyun's mathematical talents are both top-notch in the country. It is obvious that they can even draw inferences from one instance. The more Academician Wang teaches, the more comfortable he becomes, so he gives them a summary of what they have learned after graduation in the past ten years.

.

Ning Qingyun benefited the most because her original mathematical thinking was similar to that of Academician Wang. By studying the handwritten notes of Academician Wang, she had mastered the theories of the "Wang School" to a great extent. This time

With the personal guidance of Academician Wang Lao, I have made a qualitative leap, fully grasping the essence of the number theory of the "Wang School" and integrating it.

In time, when she graduates from Professor Tian Jianlan, she will become the only mathematics master in the world who can combine the knowledge of "Wang School" and "Chen School" number theory.

Even the old academician Wang Heng sighed happily: "I have taught you everything I have thought and realized in the past ten years since I retired. Especially Xiao Ning, you are the only one among my dozen disciples who have learned everything from me.

The essence of scholarship has been passed down. Even if I close my eyes and die tomorrow, I will have no regrets."
To be continued...