After chatting briefly with Ning Qingyun, Qin Ke felt happy. He shook his head, put away his mind and sat down at his desk. He opened the notes he took during today's lecture and reviewed them again.

This knowledge was recorded by himself rather than directly instilled by the system. It is easy to forget after a long time. He must fully understand it and integrate it into his own knowledge system before it can truly be used by him.

In about half an hour, Qin Ke had digested all the contents of this note and looked at the system interface.

"Mathematics level: professional level, next level: master level, upgrade progress:".

Not bad, I earned 45.5 math academic points today.

Qin Ke happily continued to study "function transformation hypergeometric system" and "group theory functional equation method". He had a vague intuition that one of these two mathematical methods would be the key to cracking Polignac's conjecture.

.

Time passed like this bit by bit, and Qin Ke's cell phone suddenly vibrated.

Qin Ke immediately put down his pen and picked up his phone. Sure enough, it was Ning Qingyun who made the video call.

Clicking to connect to the video, Ning Qingyun's familiar pretty face appeared on the screen.

Her fair and tender skin, exquisite and perfect facial features, a pair of phoenix eyes with gentle and shy water waves, and her high single ponytail made Qin Ke feel excited all of a sudden. He pressed down and wanted to kiss the screen.

Impulsively, he smiled and said, "Good morning, Jun'er."

Ning Qingyun saw the "annoying look" on Qin Ke's playful face, and suddenly remembered the two words she accidentally wrote, her face suddenly turned red, and she said slightly: "You...why are you laughing?"

"Seeing my Yun'er happy, why don't you smile?"

"You can laugh if you want, you are a bad guy anyway..." Ning Qingyun seemed to be walking around, raising her head to look at the road from time to time, but when her eyes fell on the screen, a sweet smile appeared.

"Did you just finish lunch?"

"Well, I just separated from Yan Fei and the others, and now I'm on my way to 'Little House No. 2'."

Qin Ke keenly heard the video request that Ning Qingyun sent just after he separated from his roommates. Apparently he couldn't wait to video chat with him again in the study room.

Thinking of the girl's longing and affection that were also fermented by parting, Qin Ke felt even sweeter in his heart. He said warmly: "'Little House No. 2' is far away from the girls' dormitory building and is a bit quiet. You can go there tonight."

You are not allowed to go alone."

"I know, you're not here, and I don't dare to stay there alone at night. I've been working with Yan Fei and the others these past few days, and we went to the library to study together at night. You don't have to worry about me. It's you.

When in a foreign country, you must pay attention to safety."

"Hey, I'm also safe here. By the way, you said you have an idea to prove Zhou's conjecture?"

"That's right." Ning Qingyun's dark eyes suddenly revealed a light of joy:

"I have been studying the 'Geometric Number Theory Matching Approximation Method' that you taught me recently, but I still can't figure out how to use it to prove the Polignac conjecture. On the day you left for Princeton, Yan Fei and I went to the library

During self-study, when I was helping Xiao Hui find a book, I accidentally opened a book about Zhou's conjecture."

The girl's single ponytail flicked gently, looking indescribably cute and cute: "I looked at it for a while, and suddenly an idea came to me. The 'Geometric Number Theory Matching Approximation Method' is a very excellent mathematical method specially used to solve number theory problems. I temporarily

If you can’t apply it to Polignac’s conjecture, can you apply it to Zhou’s conjecture?”

Qin Ke's mind suddenly moved, yes, he is really a fan of the authorities. He has always focused on the Polignac conjecture in order to complete the system's tasks. Why didn't he think that these new mathematical methods could be used to prove other conjectures?

I heard Ning Qingyun say in a slightly proud tone: "So I have been working in this direction for the past three or four days and have made a lot of progress. This morning I have written down all the ideas I can think of.

Okay, but unfortunately there are still a few key points that I can’t figure out, so I need you to perfect them.”

Qin Ke smiled and said, "The more you talk about it, the more curious I become."

"Just wait a moment and I'll run faster."

"Don't rush, don't fall."

Ning Qingyun said slightly: "I'm not a child, how could I fall down so easily?"

Qin Ke looked at her girlish posture that was only shown in front of him and couldn't help but be happy: "In my impression, you seem to have fallen down several times. I don't want you to fall down accidentally. There's a difference."

The boys are here to save the beauty."

Ning Qingyun pursed her lips and chuckled, her eyes longing and rippling, adding a touch of charming charm: "I won't let other boys touch me. Even if I fall, I will get up by myself. Let me ask you

Yeah, I always fell down when I was with you, did you do it on purpose?"

Qin Ke smiled: "What do you think?"

"Humph, bad guy, I guess you must be full of bad ideas. You have been thinking about making me like you all day long." Ning Qingyun wanted to put on a straight face, but when she thought about the past, she couldn't help but burst into laughter.

It's all happiness.

The two of them chatted like this without saying anything, but they felt happy from the bottom of their hearts.

When she arrived at the "Xiao Wo Er Diao" study room, Ning Qingyun quickly put down her small schoolbag, took out a notebook and opened it, with several pages filled with Juanxiu's beautiful handwriting.

"Okay, I'm going to start explaining my proof idea." The girl pointed the phone camera at the page of the notebook and pointed at the mathematical equations above with her white and tender little fingers:

"I'm sure you are familiar with Zhou's guess. I saw that you have read relevant information before, so I won't go into details. You see, my idea is that if you start with n, 2n must be an even number..."

The notebook flipped through page after page.

Ning Qingyun's voice couldn't hide her excitement: "Look, at this point, through the 'geometric number theory matching approximation method', we can basically transform it into an algebraic geometry problem, and then use the quadratic model of the objective function to

This linear approximation of (k, n) and making an effective algebraic approximation can further open up ideas..."

This chapter is not finished yet, please click on the next page to continue reading the exciting content! Ning Qingyun spoke for nearly ten minutes before saying a little embarrassedly: "Then I'm not sure how to proceed here.

The idea is to make another mathematical assumption here and start with Banach space theory. I can't think of how to do it specifically. Do you think my idea is correct?"

Qin Ke's eyes lit up when he heard this. Ning Qingyun's idea was very sophisticated. She had obviously studied the "Geometric Number Theory Matching Approximation Method" thoroughly and used it extremely skillfully. Only then could she come up with such an idea to prove Zhou's conjecture. The key is that she can

The idea of ​​using Banach space as a bridge shows that she has fully mastered the "Zhi Ning Qingjun II" number theory knowledge system tailor-made for her by Qin Ke.

Qin Ke closed his eyes and meditated for a while, then took the pen and repeatedly wrote more than a dozen lines of calculations. Finally, he raised his head and showed a bright smile to Ning Qingyun, who was looking at him uneasily on the other end of the phone:

"Jun'er, you are amazing! Your ideas are totally fine!"

He moved the scratch paper in front of the camera: "Look, I suggest that any x∈X can be taken here. As long as it is proved that there are optimal approximation elements in non-empty closed convex sets, we can match these approximation elements one by one.

Prove that the system of equations of this algebraic geometric figure has a definite solution! This proves that under even number conditions, Zhou's conjecture is true!"

Ning Qingyun's eyes were filled with admiration. Qin Ke actually figured out the problem that had troubled her for a long time in just a few minutes!

This Qin Xiaoke is really a super super math genius.

The girl lowered her eyes to prevent Qin Ke from becoming arrogant when he saw her admiring gaze, and asked again: "The proof of the odd number condition..."

"The proof of the odd number condition is much less difficult. In the nineteenth step you just mentioned, through the affine transformation of the two-dimensional homogeneous coordinates, a set of invariants are used for translation and reflection, and it is converted into algebra

For geometric problems, we should be able to prove it by using the approximation matching method!"

"That is to say," Qin Ke said with certainty and excitement: "Jun'er, Zhou's conjecture will soon be proven in our hands!"

"We? But I only provided ideas, and only two-thirds of the proof ideas under even numbers..." Ning Qingyun knew clearly that although she had come up with some ideas, she wanted to turn these ideas into a specific argumentation process.

, it was very difficult, at least she didn’t have the confidence to write it.

"Of course, this is the result we made together. Without your ideas, I wouldn't have been able to prove it in two years! This is a project we worked on together, called 'Qin Ke and Ning Qingyun's Zhou Conjecture Proof Project'

alright!"

Ning Qingyun felt sweet in her heart. Qin Ke's recognition and affirmation made her finally feel like she could stand beside him with her head held high.

Not only was he pulling me forward, I was also able to give him some boost.

This filled Ning Qingyun's heart with a sense of accomplishment and joy.

"Jun'er, in the past two days, you should try to write out the proof process of Zhou's conjecture according to the ideas I just completed. This will be very helpful to improve your mathematical ability."

"But... I'm afraid that I don't have the ability to finish writing the entire argument process..."

"It doesn't matter, just write everything you can, and leave the rest to me. I... will try to follow your idea and see if I can use the 'geometric number theory matching approximation method' to prove a few more conjectures!

Let’s not touch the big BOSS like Polignac for the time being. Let’s attack the other small BOSS first, save more experience points, and then deal with it after it has been upgraded!”

Ning Qingyun looked at his confident and arrogant expression, couldn't help but pursed her lips and said with a smile: "You thought you were playing games and saving some experience points to upgrade."

Qin Ke smiled. For him, what he earned was not experience points, but academic points, but he could indeed upgrade.

He remembered what he had seen and heard at Princeton University yesterday, took a deep breath, and said firmly: "Jun'er, come on, we two must try to solve a few small conjectures together. Look at the foreigners who make people look down on our Xia country, let's

The mathematicians of the Xia Kingdom are no less than the mathematicians of any other country!"

"Yeah." Ning Qingyun lowered her eyes again. Every time she saw such a confident and domineering Qin Ke, she would have the urge to kiss him.

"By the way, you... need to go to bed early, it's already one o'clock in the morning."

Qin Ke blinked: "Okay, but you have to kiss me first."

Ning Qingyun's face turned red again: "Kiss... I can't kiss you."

"Would it be okay to say 'Mua'? Or maybe 'Baji' would be fine too."

Ning Qingyun shook her head vigorously: "I...I won't..."

Qin Ke looked like a scoundrel: "I won't learn it now. Anyway, if you don't kiss me, I won't sleep. I'll go to the lecture tomorrow with panda eyes and yawning, and then maybe I'll be at the venue again."

I was kicked out of the venue because I was snoring and I was humiliated... Do you feel distressed when you think about it?"

"...Bad guy." Ning Qingyun blushed and clicked on the screen.

"Hey, Jun'er, what are you doing..." Qin Ke continued to fight, but the video was interrupted.
To be continued...