From Almighty Scholar to Chief Scientist

Mr. Xu should give him advanced algebra questions, right?

But this question doesn't look like a question in the direction of advanced algebra?

Obviously it is a number topic, and of course number theory can also be solved with knowledge of algebra.

So is polynomial?

matrix?

Or spatial or linear functions?

The questions the teacher gave him couldn't be unsolved math problems, could they?

It is definitely possible to solve it, but it is a bit difficult...

So, he thought hard for 5 minutes like this, and at the same time performed a simple calculation on the draft paper.

In calculus, we must first list the laws of this sequence of numbers.

Lin Xiao listed the first few items of the sequence.

1, 1, 2, 3, 5, 8, 13, ...

Seeing these series of numbers, he was taken aback for a moment. This series of numbers seemed familiar. After a quick thought, isn't this the Fibonacci series?

No wonder, when he looked at this general term formula, he felt a little familiar.

The Fibonacci sequence, named after the Italian mathematician Leonardo Fibonacci in the twelfth century, is defined recursively in mathematics: the zeroth and first terms are specified After being 0 and 1 respectively, each of the remaining items is equal to the sum of the first two items, and the zeroth item is a special item and is not included in the sequence.

You may think that this sequence looks ordinary, isn't it such a simple law, I can also create a sequence.

For example, it is called the Zhangsan/Outlaw Fanatics sequence, which stipulates that the first three items are 1, and each of the remaining items is equal to the sum of the first three items, or the first four items are stipulated.

However, the reason why the Fibonacci sequence is special is that it is not so simple. The Fibonacci sequence is also called the golden section sequence. The value of the previous item divided by the next item will get closer and closer Based on the golden ratio, which is 0.618.

In addition, there are many coincidences in this sequence in nature. For example, 99% of the spiral arrangement of sunflower seeds obeys the Fibonacci sequence, and the growth law of branches also conforms to this sequence.

Therefore, there are many mathematicians who study the Fibonacci sequence.

However, this Fibonacci prime problem...

Lin Xiao was confused.

Isn't this really an unsolved problem in mathematics?

But this is a question the teacher gave me...

It's impossible for Mr. Xu to cheat him on purpose, right?

Or, he took the wrong question?

Why don't you search your phone?

But after thinking about it, if this question has been solved, wouldn't he be considered to know the answer in advance?

For him, even seeing an idea is of great help to solving problems.

Lin Xiao didn't know that this was indeed an unsolved problem, because he didn't study the Fibonacci sequence, and he knew that the formulas of the general terms of this sequence were all calculated, so how could he understand these side details?

Moreover, this problem is not well-known. The unsolved mathematical problems generally known to middle school students in Huaguo are basically limited to Goldbach's conjecture, because there is a mathematician named Chen in Huaguo who solved Goldbach's conjecture. The "1+2" ​​problem, so for the purpose of propaganda, this problem was written in the mathematics textbook and told to the elementary and middle school students in Huaguo.

As for the more famous problems in mathematics, such as Riemann conjecture, BSD conjecture, Hodge conjecture, etc., not many primary and middle school students know it.

So Lin Xiao got tangled up and didn't know how to deal with this question.

But suddenly, a light flashed in his mind.

This question is written on the third piece of paper!

And the questions on the first paper are obviously easier than the questions on the second paper. From this point of view, the questions on the third paper must be more difficult than the second paper.

But the question on the second sheet was already difficult enough, and there was only one question on the third sheet, which was even more difficult, obviously it should be taken for granted.

This logic is easy to figure out!

Lin Xiao immediately stopped being entangled, and at the same time respected Teacher Xu Hongbing.

This kind of control over the difficulty of various topics before and after is really amazing!

As expected of a professor of mathematics.

So he stopped thinking too much and continued to think about his ideas.

In this way, 1 minute passed, 2 minutes passed, and 10 minutes passed.

Endless storms had already set off in his mind, and the synapses at the nerve endings released transmitters at a high frequency, causing his brain to start operating at an extremely deep level.

Soon, he had a flash of inspiration, if it is a polynomial...

He immediately started writing on the draft paper.

First write its general term formula as An-(An-1)-(An-2)=0.

"Then you can use the method of solving the second-order linear homogeneous recursive relation, then its characteristic polynomial is..."

[The characteristic polynomial is: λ^2－λ－1=0】

【得λ1=1/2（1＋√5），λ2=1/2（1－√5）】

【即有An=c1λ1^n＋c2λ2^n，其中c1，c2为常数，我们知道A0=0，A1=1，因此……】

【最终解得c1=1/√5，c2=－1/√5。】

[Introduce the prime number theorem here, π(x)=Li(x)+O(xe^(-c√lnx)(x→∞), where Li(x)=……]

After writing this, Lin Xiao fell into thinking again.

Next, he will try to combine the two.

As long as the two can be combined, then he has completed the proof.

Because, the prime number theorem is obviously based on the conclusion that there are infinitely many prime numbers, as long as the two can be contained, and the area is infinite, then the conclusion can be drawn.

That is to say, if one is proved to be large, then the small one will naturally complete the proof.

But obviously, it is not easy to combine the two and find the connection point, and more processing is needed in the middle.

"They need to be changed, the relationship between the two is too far away now..."

Lin Xiao stroked his chin, thinking about how to transform them equivalently.

At this moment, he felt a pat on his shoulder.

"Lin Xiao? Lin Xiao?"

He recovered and looked to the side.

It's Kong Huaan.

"what happened?"

Lin Xiao asked.

"It's almost twelve o'clock, don't you rest yet?"

"Huh? Is it twelve o'clock?"

Lin Xiao realized that it was very late, even if he didn't take a rest, Kong Huaan still had to.

So he could only temporarily give up and continue thinking, nodded and said: "Well, I'm going to rest."

Then he closed the draft paper and went to wash. After washing and returning to the bed, he was still thinking about how to prove it next.

Gradually, however, he fell asleep.

No way, he fell asleep on the bed.

Chapter 43 Sage Status

"The process of solving unsolved problems is the process of developing new mathematical methods. It is a coincidence to use old methods to solve mathematical conjectures, but using new methods to prove mathematical problems will add vitality to the mathematical community. A mathematician is committed to doing it, you know?"

"One thing to say, indeed."

"Then, Lin Xiao, I hope you can go further and further on this road."

……

Lin Xiao suddenly felt his consciousness return to the darkness.

Strictly speaking, it wasn't darkness, it was just his eyes closed.

He wanted to open his eyes, but his eyelids felt numb, or the upper and lower eyelids were stuck together, making it difficult to open them.

Of course, it's okay to overcome a little bit.

After rubbing his eyes and feeling a little better, he got up from the bed.

"Ah~~"

Yawning, he remembered that he had just had a dream.

It seems that Mr. Ding Ping taught him the truth, but it seems to be the mathematics teacher of science class one, or Professor Chen Song, Professor Xu Hongbing, etc. I don't remember clearly, but he still remembers the truth taught, probably Speaking of solving mathematical problems, we need to try to create some new mathematical methods.

Using existing mathematical methods to solve those unsolved problems is not the value of these problems. It can only show that the corner that no one has discovered happened to be discovered by you, but in a long time, this corner will be hidden sooner or later. people found out.

For the mathematics community, although it solves a regret, it does not make the mathematics community better as a whole, because the mathematics community is still the same, and there are no innovative things. Some people are worse, because the subject of some students may just happen to be the problem you are studying, and you solve it. It took someone who didn’t know how long to do the research, or even the graduation thesis. This is good, and they all graduate no more.

Lin Xiao thinks this statement is very reasonable. Mathematics is the most basic subject in all scientific research in the world. It needs to be continuously developed so that it can bring more places where it can be used in the world.

However, Lin Xiao did not dwell on this matter. He would later prove that there are infinitely many prime numbers in the Fibonacci sequence. This is not an unsolved problem.

As for the problem of solving unsolved problems, it is not for him, an ordinary student who will not be an adult for a month, to consider.

Soon, after washing up, Kong Huaan also woke up. He was going to a training class later, after all, he paid for it, and it would be a waste if he didn't attend the class.

For Lin Xiao, there is no need to attend classes. He is not interested in those classes. They are all about Mathematical Olympiad anyway, and Mathematical Olympiad is no longer his problem.

Afterwards, I went downstairs to the restaurant with Kong Huaan to have breakfast, and went back to the hotel to check the time. It was not until 08:30, which was still early, but Lin Xiao didn't waste time. He sat at the table and continued to study Reminds me of the question from last night.

According to the train of thought that he thought before going to bed last night, he entered the state of immersion again.

But even so, after trying various methods, he still found that there was too much difficulty, and there seemed to be an insurmountable gap, preventing him from combining the two formulas listed last night.

For the first time he felt a sense of disorientation.

This was the first time he encountered such a difficult problem after he got the system, especially this problem was given to him by the teacher.

His thinking began to become chaotic and he fell into cranky thoughts.

"Would you like to spend a little time?"

"Forget it, it's a lie, and I'm too embarrassed to explain it to Mr. Xu."

"But, this is too difficult!"

He has been thinking for three hours, even if he has finished the CMO test questions for a day, and now he has no idea at all.

"By the way, I remember that truth points can also be used to solve these problems?"

Lin Xiao suddenly remembered this matter, so he asked in his heart: "System, how many truth points are needed to solve this problem?"

System: "According to the host's current math level (Level 1), 3 truth points are needed to solve this problem."

"3 truth points, then I now have 4.2 truth points, isn't it just right?"

But Lin Xiao suddenly came to his senses, wouldn't there be no difference between using the truth points and copying the answers?

He immediately patted himself on the head, "Lin Xiao, Lin Xiao, don't think about getting something for nothing all day long, how can you find the truth in the future like this?"

"Don't think about it so much, at worst, just honestly admit to the teacher that you can't do it at night."

"But having said that, this kind of question actually needs 3 truth points, and this truth doesn't need to be spent at all."

With a mutter in his heart, Lin Xiao pulled himself together and thought about a solution to this problem.

But in the end, apart from writing down a bunch of meaningless calculations on the scratch paper, he still couldn't find any good method.

Lin Xiao scratched his head, feeling a little crazy.

"It would be great if the development of the brain can be improved..."

"Huh? Brain development?"

Lin Xiao suddenly remembered that the system had previously rewarded him with something called [Sage State], which was used to increase his brain development by 50%.

"Yeah, I actually forgot even this."