Xueba starts with change

Chapter 203 Starting from the Digital Pyramid

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

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

Chen Zhou unconsciously thought of the digital pyramid.

This is also his greatest achievement.

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

After getting off the car, Chen Zhou went straight to the dormitory, he couldn't wait.

As a result, the team leader teacher was still counting the number of people, and was about to say something, but Chen Zhou's figure had disappeared.

Of course, Chen Zhou didn't just turn his head and leave. He told Li Li that if he counted the number of people, he would speak up for him.

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

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

He is chasing the footsteps of the earth turning.

"List out the digital pyramid first."

Library, old location.

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

"The next step is based on the calculation of the hail conjecture."

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

【把奇数a经过m次的冰雹猜想运算后，得到的第m+1个奇数记为a(m)，显然会有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, we can list the m+1 odd numbers obtained by a after m times of hail conjecture operations: a, a(1), a(2),..., a(m)]

After writing this, Chen Zhou looked back at the model of the digital pyramid.

Between the two, it can be connected in series.

In the digital pyramid, Chen Zhou marked the positions of the m+1 odd numbers obtained by a after m times of hail conjecture operations.

Then use a one-way arrow to start from a(n) to a(n+1), and connect these points in turn.

After finishing these, Chen Zhou looked at the digital pyramid and wrote next to the curve with a pen:

[Odd number, the route Lm after hail conjecture calculation]

"Well, regarding the route, we must be clear..."

Chen Zhou habitually tapped the draft paper with a pen, thinking about the route.

After verifying the route in his mind, Chen Zhou began to write:
[If ab is divisible by 2 sequentially in m times of hail conjecture operations b1, b2, b3, ..., bm times, ac is divisible by 2 in sequence c1, c2, c3 in m times of hail conjecture operations, ..., cm times ...]

【...When the condition br=cr (r=1, 2, 3, ..., m) is established, it can be said that ab and ac have "the same calculation route".When the condition br=cr is not necessarily true, but r=1→m∑br=r=1→m∑cr is true, it can be said that ab and ac have "similar calculation routes". 】

So far, Chen Zhou has completed the preparatory work.

Looking at what he had written on a whole piece of draft paper, he couldn't help showing a smile on his lips: "This line of thinking is tricky..."

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

Just after the military training, he came to the library to solve the hail conjecture, and there was no one else but 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 beside her with a backpack and a lunch box.

Well, Yiyi is also tanned, is that sunscreen fake?
Before Chen Zhou thought of the military training, he did a search and prepared a military training strategy for Yang Yiyi.

But looking at Yang Yiyi's face, Chen Zhou immediately felt that this strategy was unreliable, thanks to hundreds of people's praises.

"Hey, come here without eating at noon, do you want to cultivate immortality?" Yang Yiyi handed the box lunch to Chen Zhou, with a hint of blame in her tone.

Chen Zhou took the lunch box and promised in a low voice, "It won't happen next time."

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

After finishing speaking, regardless of Yang Yiyi's reproachful eyes, she got up and walked away with the lunch box.

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 with his departure, the cough that was already ready to go was suppressed again.

The dishes Yang Yiyi bought for Chen Zhou were all his favorites.

Satisfied, Chen Zhou wiped out the box lunch full of happiness.

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

Looking at Yang Yiyi's back, Chen Zhou thought for a while and went out again.

When he came back, he had a bowl of ice cream in his hand.

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

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 pampered her head.

Yang Yiyi pouted, turned to look at Chen Zhou: "It's delicious~"

Chen Zhou smiled softly.

Putting aside the previously filled draft paper and taking out a new draft paper, Chen Zhou continued his research on the conjecture of hail.

From the digital pyramid, we can also obtain some characteristics of the nth level odd number when performing hail conjecture operations.

【特性1：若对数字金字塔中第n级的2^(n-2)个奇数均进行一次冰雹猜想运算，将有2^(n-3)个奇数在进行冰雹猜想运算时，仅能被2整除1次；以此类推，有1个奇数在进行冰雹猜想运算时，能被2整除n+d(n)次，这里的d(n)等于1(n奇数时)或-1(n为偶数时)】

This is what Chen Zhou thought about during his military training.

But feature 1 needs proof.

After a brief thought, Chen Zhou proceeded to prove it.

The method of proof is not difficult, and some content of number theory is required.

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

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

This is an arithmetic progression with a tolerance of 2.

Using this feature, the sequence can be converted again.

That is, the form a2=a1+2 is 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 calculation on the items in the above formula, you should first multiply each item by 3, and then add 1 to get...]

The pen in Chen Zhou's hand didn't stop for a moment, following his train of thought, he calculated every item.

再把运算之后的每一项进行简单的变化，把3·2看作是a，3a1+1看作是任意整数b。

At this point, it can be deduced according to the number theory lemma on the side.

【……序号为2^(n-4)+2^(n-6)+……+2+1的项乘以3再加上1后为……】

[Therefore, this formula can be divisible by 2 n+1 times.From this, it can be seen that the description in characteristic 1 is correct. 】

(End of this chapter)