The characteristic 1 of the n-level odd number when performing hail conjecture operation is proved.

But Chen Zhou's pen did not stop.

Take out a new piece of draft paper, and the pen tip starts to have close contact with the paper.

He planned to continue to study the hail conjecture in one go.

At least, various thoughts during military training.

He needs to be fully released.

[Property 2. If the first hail conjecture operation is performed on the nth level in the numeric pyramid, the 2^(n-3) term that can only be divided once by 2 will continue to perform the second hail conjecture operation.]

[There are 2^(n-4) items that can only be divisible by 2 once, 2^(n-5) items that can only be divisible by 2 times, and 2^(n-6) items that can only be divisible by 2 times,

Dividing 3 times,..., 2 items can only be divided n-4 times by 2, only one can be divided n-3 times by 2, and the other item can be divided n-2 times by 2 or more.

】

[If you continue to perform hail conjecture operation on the nth level in the digit pyramid, when performing hail conjecture operation for the first two times, the 2^(n-4) term that can only be divided once by 2 will continue to perform the third hail conjecture operation...]

Chen Zhou browsed the characteristics of the n-level odd numbers obtained from the pyramid of numbers 2 when performing hail conjecture operations.

The handwriting filled a whole piece of a4 draft paper.

These contents are what Chen Zhou thought about.

The characteristics of the nth level odd number when performing hail conjecture operation are extended step by step to general form.

Regarding the proof of feature 2, Chen Zhou also started proof from the first hail conjecture operation.

Chen Zhou took a chance here.

He linked feature 2 and feature 1.

The same is used to prove it using sequences.

In this way, there will be:

[…… When performing hail conjecture operation for the first time in level n, the terms that can only be divisible by 2 are: a2, a4, a6,..., a2r,..., a2^(n-2).]

[In this sequence, the interval distance is 2 items and the tolerance is 2^2, so the sequence can be written as a2, a22^2, a22·2^2,..., a2r·2^2,...,

The form of a2(2^(n-3)-1)·2^2...]

According to this idea, Chen Zhou performed the first hail conjecture operation of the new form of sequence and then performed the second hail conjecture operation.

Looking at the obtained calculation results, Chen Zhou thought for a while and converted it.

[Think 3^2·2 as a, 3a2(1)1 as any integer b...]

After the conversion was completed, Chen Zhou's ideas became clearer.

He glanced at the two number theory conclusions written in order to prove the characteristic 1, which also needed to be used in the process of proving characteristic 2.

Using these two number theory conclusions, Chen Zhou easily inferred that "In the above formula, any adjacent 2^r (here 0≤r≤2^(n-3)) terms can be 2

^(r1) Divide”.

As a result, Chen Zhou completed the first step in proof of Feature 2.

This is also the most important step.

With the first step of laying the groundwork, it will be much easier to prove the general form step by step.

The thoughts are constant, as stable as an old dog.

The pen in my hand is constantly on the draft paper, turning the thoughts in my mind into reality one by one.

This is an extremely refreshing feeling.

[…… From this we can infer that the general form of feature 2 is correct.]

At this point, Chen Zhou has completed all the preparations for proving the hail conjecture in the early stage.

And these conclusions are all obtained using the digital pyramid.

Chen Zhou put down his pen and looked at the time. It was already 3 pm.

"I didn't expect that the two characteristics that look simple and have smooth thinking have taken me so much time..."

He murmured to himself, Chen Zhou stopped thinking too much, calmed down his thoughts, sorted out the previous draft paper, and took it in his hand and stroked it.

This is to make Chen Zhou clearer in order to understand his ideas.

Because the proof idea triggered by the digital pyramid occurred during military training, there may be some details in it, which Chen Zhou did not consider.

Therefore, it is necessary to make up for one's own ideas.

Moreover, in the face of world-class problems, Chen Zhou felt that it would not be an exaggeration to be more cautious.

This is also why he was praised for his extremely rigorous calculations.

Put down the draft paper and take out a new draft paper.

Chen Zhou once again entered the world of proof of hail conjecture.

First of all, Chen Zhou needs to perform formulaic conversion.

That is, the proof of the hail conjecture is converted into a narrative form that is more in line with his current proof method.

The transformation of narrative form also transforms the proof form of hail conjecture.

Of course, this form of proof is to rely on Chen Zhou’s previous preparations.

Therefore, Chen Zhou needs to prove first that "all odd numbers at level n in the pyramid of numbers can be calculated by finite hail conjecture, and become an odd number smaller than itself (n is any positive integer, n>56)

”, this conclusion.

Formulating the conclusion is a necessary process for proof.

[Suppose the odd number a(>56) has passed m hail conjecture operations, and its form is a(m)=3^m/2^(b1b2b3...bm)a3^(m-1)/2^(b1b2b3...

…bm)3^(m-2)/2^(b2b3…bm)…3/2^(bm-1bm)1/2^bm】

[When the power index of the denominator in the first term coefficient 3^m/2^(b1b2b3...bm) in the above formula appears for the first time b1b2b3...bm≥2m...]

[… Therefore, it can be determined that the odd number a can become an odd number smaller than itself through several hail conjecture operations, referred to as a for short, meeting the condition "a>a(m)".]

After the formula is completed, it is a proof of the conclusion.

This step is not that brain-related.

With the early preparation, Chen Zhou was much more relaxed when proofreading the "calculating method of odd numbers in the nth level of "meeting the condition a>a(m)" either in terms of thinking or calculation.

Especially Chen Zhou's use of Feature 1 and Feature 2 can be said to have supported the entire verification process.

Combined with the content of the numerical pyramid, Chen Zhou compiled a table about "what numbers that meet the conditions a>a(m)" obtained each time when odd numbers are continuously performed in the nth level.

The first operation, the second operation, and the odd numbers after the first term coefficient of the m-th operation are listed in detail.

In the column of the m-th hail conjecture, the rules are obtained by using the operation routes similar.

After completing the proof of this part of the content, the sky outside has already darkened.

When Chen Zhou put down his pen again and was about to stretch, he realized that it was already seven o'clock in the evening before he knew it.

He glanced at Yang Yiyi beside him and was looking at the textbook.

Yang Yiyi felt something and turned her head to look at Chen Zhou.

She smiled at Chen Zhou and said softly: "Let's go, come back after dinner?"

Chen Zhou nodded: "Have you been waiting for me for a long time? Why don't you call me?"
Chapter completed!