After saying goodbye to the instructor, the teachers and students who participated in the training returned to the school by car.

In the car, when the team leader asked Chen Zhou what impressed them the most about this military training.

Chen Zhou unconsciously thought of the digital pyramid.

This is also his biggest gain.

Now that the military training is over, he can finally pour out all the thoughts in his head.

As soon as he got off the bus, Chen Zhou went straight to the dormitory, he was a little impatient.

So much so that the team leader and teacher were still counting the number of people, ready to say something more, but Chen Zhou's figure had disappeared.

Of course, Chen Zhou didn't turn around and leave, he told Li Li that if the number of people was counted, he would help him squeak.

On the way, Chen Zhou sent another message to Yang Yiyi, telling her that he would wait for her in the library in the afternoon.

However, Chen Zhou himself returned to the dormitory, packed his things, and went directly to the library.

He was chasing the footsteps of the Earth turning.

"Let's start with the pyramid of numbers. ”

Library, old location.

Chen Zhou took out the scratch paper, began to draw triangles, and then graded them, listed the numbers at each level, and completed the construction of the digital pyramid model.

"What follows is an operation based on the hail conjecture. ”

Thinking like this, Chen Zhou, with the pen in his hand, continued to write on the scratch paper.

[After the odd number a is calculated by m hail conjectures, the m+1 odd number obtained is recorded as a(m), and obviously there will be a(m)=3^m/2^(b1+b2+··· +bm)·a+3^(m-1)/2^(b1+b2+··· +bm)+3^(m-2)/2^(b1+b2+··· +bm)+··· +3/2^(bm-1+bm)+1/2^bm】

[Here you can list the m+1 odd numbers obtained by a after m hail conjecture operations: a, a(1), a(2),...... ，a(m)】

Writing this, Chen Zhou looked back at the model of the digital pyramid again.

Between the two, it can be connected in series.

In the number pyramid, Chen Zhou marked the location of the m+1 odd number obtained by a after m hail conjecture operations.

Then use a one-way arrow to point from a(n) to a(n+1) and connect the dots in turn.

After doing this, Chen Zhou looked at the number pyramid and wrote next to this curve with a pen:

[Odd number, route Lm after hail conjecture operation]

"Well, on the question of the route, it must be clear ......"

Chen Zhou habitually pointed at the scratch paper with his pen, thinking about the route.

After completing the verification of the route in his mind, Chen Zhou began to write:

[If ab is divisible by 2 in the hail conjecture operation of m times, b1, b2, b3 in turn,...... , bm times, ac can be divisible by 2 in order of 2 in the hail conjecture operation of m times, c1, c2, c3,...... , cm times ......]

【...... When the condition br=cr(r=1,2,3,...... , m) can be said to be "the same line of operation" as AC when it is true. When the condition Br=Cr is not necessarily true, but R=1→m∑br=R=1→m∑cr is true, AB can be said to be "similar to the line of operation" of AC. 】

So far, Chen Zhou has completed the preliminary preparations.

Looking at the content of a whole sheet of scratch paper, the corners of his mouth couldn't help but show a smile: "This idea has a ...... to do something."

Putting down the pen, Chen Zhou stretched his waist, a little tired.

As soon as he finished participating in military training, he came to the library to solve the hail conjecture, and there was no one else except him.

"Little brother, what were you laughing at just now?"

Hearing this familiar voice, Chen Zhou tilted his head slightly, and saw Yang Yiyi standing next to him with a backpack and a boxed lunch.

Well, Yiyi also got a tan, could it be that sunscreen fake?

Before Chen Zhou thought of military training, he also deliberately searched for it and prepared a military training strategy for Yang Yiyi.

But looking at Yang Yiyi's face, Chen Zhou suddenly felt that this strategy was unreliable, and it was still liked by hundreds of people.

"Now, come here without eating at noon, do you want to cultivate immortals?" Yang Yiyi handed the boxed lunch in his hand to Chen Zhou, with a hint of blame in his tone.

Chen Zhou took the lunch box and promised in a low voice: "Not next time." ”

After a pause, he added: "Who let me have such a caring girlfriend." ”

After speaking, regardless of Yang Yiyi's disgusted eyes, he got up and walked into the distance with a boxed lunch.

After all, the self-study area in the library is still not easy to eat directly.

He was afraid of being beaten.

But what Chen Zhou didn't know was that as he left, the cough that was already ready to go was taken back again.

The dishes that Yang Yiyi bought for Chen Zhou are all what he likes to eat.

Chen Zhou was satisfied to eliminate this box lunch full of happiness.

After cleaning up the garbage, Chen Zhou slowly walked back to the self-study area.

Looking at Yang Yiyi's back, Chen Zhou thought about it and went out again.

When he returned, he had an ice cream bowl in his hand.

Gently patted Yang Yiyi's back, and when Yang Yiyi turned his head, Chen Zhou handed over the ice cream bowl: "Na." ”

Yang Yiyi happily took it, eating ice cream while looking at the book in her hand.

Chen Zhou looked at Yang Yiyi's appearance and rubbed her head dotingly.

Yang Yiyi pouted, turned her head and looked at Chen Zhou: "It's delicious~"

Chen Zhou smiled softly.

Putting aside the scratch paper that had been written before, and taking out a new scratch paper, Chen Zhou began to continue his research on the hail conjecture.

From the number pyramid, some characteristics of the nth odd number can also be obtained when performing hail conjecture operations.

[Feature 1: If the hail conjecture is performed once on all 2^(n-2) odd numbers of the nth level of the number pyramid, there will be 2^(n-3) odd numbers that can only be divisible by 2 by 1 time when the hail conjecture is performed; and so on, there is an odd number that can be divisible by 2 by n+d(n) times when the hail conjecture is performed, where d(n) is equal to 1 (when n is odd) or -1 (when n is even)]

This is what Chen Zhou thought about when he was in military training.

But feature 1 needs to be proven.

After a brief thought, Chen Zhou set out to prove it.

The method of proof is not difficult, and it requires a part of number theory.

Chen Zhou first wrote down the content of number theory that needs to be used, and then listed the 2^(n-2) odd numbers in the nth level of the number pyramid in turn.

Then make them equal to a1, a2, a3,...... ，a2^(n-2)。

This is a series of equal differences with a tolerance of 2.

With this feature, the sequence can be converted again.

That is, the form of a2=a1+2, to be converted.

After the conversion was completed, Chen Zhou tapped the tip of the pen, thought for a while, and wrote:

[When performing the first hail conjecture on each item in the above formula, you should first multiply each of them by 3, and then add 1 to get ......]

The pen in Chen Zhou's hand did not stop for a moment, and he followed the train of thought and calculated each item.

Then make a simple change of each term after the operation, and 3·2 is regarded as a, and 3a1+1 is regarded as any integer b.

At this point, you can deduce according to the number theory lemma on the side.

【...... The term with the serial number 2^(n-4)+2^(n-6)+......+2+1 multiplied by 3 and 1 is ......]

[Therefore, the formula is divisible by 2 by n+1 times.] This shows that the statement in Trait 1 is correct. 】