An Expert Is actually By My Side

Chapter 37: This question is simple!

Translator: Henyee Translations Editor: Henyee Translations
“You should be more honest. If you’re late, you’re late. Can’t you openly enter through the front door?”
F*ck!
Isn’t it because I’m afraid that it’ll interrupt your class?
Then again, isn’t it an international practice to enter through the back door when you’re late?
At once, countless pairs of eyes turned to him. Even if he was considered relatively thick-skinned, Cloud Hao was still a little embarrassed.
Just as he was hesitating to enter again through the front door, Li Xuesong, who was on the stage, coughed and continued with a straight face, “Where’s your assignment?”
Assign-assignment?
When he heard these words, Cloud Hao’s expression instantly turned uneasy. “Uh, I forgot to bring it.”
Forgot to bring it?
Hurr hurr!
If you didn’t do it, you didn’t do it. What’s more, you’re using such a crappy excuse.
Li Xuesong stared at Cloud Hao with an insincere smile. He chuckled and continued, “Forgot to bring it? That’s fine. So, it means you did it, didn’t you? Anyway, it’s just one question. You can write your answer out now, right?
With that, he tapped his index finger on the blackboard. “Come up here to write.”
The class became restless upon hearing the old professor’s words. Many students began whispering to one another.
Cloud Hao, standing in the back row, couldn’t hear what they were talking about. He just wanted to complain that the old professor had lost it today. It wasn’t as if he had committed some bloody atrocity that cried to Heaven. He was just one or two minutes late; was it really necessary for the professor to be so hard on him?
When he noticed Old Li’s sarcastic smile, he knew he was doomed today.
After chewing out the fool that stole his notebook in his heart, Cloud Hao sighed. He ultimately trudged towards the board.
As he passed the front row, he noticed Zheng Xueqian frantically signalling with his eyes and vigorously jabbing his phone screen, as if trying to hint to him to read his WeChat.
[Are you crazy?! You actually went up? No one can answer that question!]
Although he could guess that this good pal of his had probably sent him the answer to the assignment, he had walked up to the podium now. He obviously didn’t have any chance to take out his phone.
Cloud Hao flashed him a look of assurance and communicated with his eyes. Relax, I’m fine.
When he met that “confident” gaze, Zheng Xueqian was stunned for a moment.
What the f*ck?
What does this guy mean?
Can it be that… he really solved it?
Impossible!
The question that even Expert He couldn’t solve…
The meeting of gazes was just for a fleeting moment. Before Zheng Xueqian could confirm whether he had misunderstood Cloud Hao’s meaning or not, he could only watch him going up the lectern.
Cloud Hao took the chalk from Old Li’s hand and stood in front of the blackboard for a while. Then, all of a sudden, he turned around in mild embarrassment.
“Uh, what’s the question again… I didn’t memorize it.”
Li Xuesong instantly smiled and gestured to the lectern with his chin. In his heart, though, he was waiting for a show. Let’s see how long you’re going to keep up this act.
“There are so many on the lectern. You can just copy from one.”
It’s okay to copy from one…
Aren’t you afraid that I will look at the answer?
Cloud Hao muttered inwardly as he picked up the assignment at the top. Then, within a second of flipping it open, he was taken aback.
My God. This person only wrote the word “solution”.
Does he not want his class grades?
At least, hide the paper towards the bottom!
He took a look at the name again and realized that it actually belonged to Liang Ziyuan.
After silently taking note of the question, Cloud Hao loyally helped him stuff his workbook at the bottom.
Li Xuesong noticed his little trick, but he simply chuckled without exposing him. He raised his eyebrows and said, “Do you know what the question is now?”
“Uh, I remember now.”
“You remember? Alright, enough talking and start writing!”
It was not a particularly difficult question at the start, and in fact, there were only a few alphabets in there. All the information about the question stem could be stated clearly in two sentences.
Cloud Hao didn’t think too much about it. He turned around and copied the question onto the blackboard. Then, he reread the question from beginning to end.
However, it was fine until he wrote it down. It was when he had finished writing and read the question again that he froze on the spot.
[Suppose positive integers a and b satisfy (a2+b2)/(ab+1)=k∈N, prove that k is the square of a certain positive integer.]
Oh my.
This question…
Looks a little familiar?
Li Xuesong assumed that Cloud Hao didn’t know the answer, as he hadn’t moved in a long time. Hence, he smiled and joked, “If you can write the answer, you won’t have to attend my classes in the future. I’ll still give you all the credits.”
Cloud Hao gulped and asked in disbelief, “…Really?”
“Heh, why would I lie to you?”
In that case, I’ll really write out the answer…
After confirming that the professor wasn’t joking, Cloud Hao hesitated for a moment. He finally put the chalk on the blackboard and started writing.
[Assuming that k is not the square of a positive integer, then a≠b.]
[Considering the indeterminate equation a2-kab+(b2-k)=0, if a=b, then k=1 can be deduced, which contradicts the assumption.]
[Therefore, let us set a>b>0 and take a set of solutions (a0, b0) to minimize a0+b0…]
Although he had copied this question in the rough notebook previously, Cloud Hao never took the time to carefully study it. If he did, he wouldn’t have been stunned on the spot.
The reason for his shock was simple.
It was because not only was this an original question, but it was also the sixth question in the IMO International Mathematics Competition in 1988 on the earth in his previous life!
As for why he knew that…
It wasn’t because he had participated in the competition that year, but because just yesterday, he had seen it in the advanced mathematics textbook filled with notes. He even did it once for himself at the end.
He even remembered that this question was written down in the blank space at the end of the page of Vieta’s formulas.
According to Professor Lu’s slightly derisive annotation, no one from the main examination committee could answer this seemingly simple number theory problem. In the end, they sought the help of four number theory experts from Australia, the host of the competition. Even then, they were unable to find a solution for a long time.
Since the experts couldn’t solve this problem within the stipulated time, this problem, therefore, became a legend.
There were hundreds of participants, and only a dozen or so managed to solve it. One of them even won a special prize from the main examination committee of the competition for his exceptional answer.
Right now, the solution he was writing on the blackboard was the “model answer” that was awarded the special prize.
The interesting thing was that according to Professor Lu’s notes, the dozen or so contestants who managed to figure out the solution eventually became well-known figures in the mathematics field. While commenting on this past that was a secret to all but a few, the professor also lamented.
[Under normal circumstances, mathematics is a product of intuition, but some counter-intuitive propositions cannot be ruled out. Just as our common sense always tells us that proof by contradiction is unreliable, our common sense can also occasionally be counter-intuitive and deceive us.]
[I was a little surprised that even Tao Zhexuan, who shouldn’t lose to this question, was unfortunately defeated by it.]
Although Cloud Hao didn’t have any particular interest in mathematics and had never even heard of that professor’s name, he still came to a reliable conclusion from that annotation written on limited space.
This notebook is probably a belonging left behind by a famous or even important figure in my previous life?
When he thought about this, it suddenly felt like a holy relic.
It was a pity that after he had finished reading the notes, the system didn’t even leave him a single speck of ash. It simply erased the existence of that thing from the world.
As Cloud Hao let his imagination run wild while writing down the answer on the blackboard based on the reasoning for the solution in his memory, Professor Li Xuesong, who was standing next to him, was dumbstruck.
It was okay if he was just writing gibberish. At most, after this guy finished, he would mock him from the side—Uh no, utter a few words of criticism to educate him.
Yet, he couldn’t find a single mistake in this guy’s solution so far at all!
He even felt that…
It actually seemed to make sense?!
Especially when Cloud Hao reached the fourth line, his entire expression changed.
What the f*ck?!
This question could actually be solved like this?
He was not the only one who was shocked. He Ping standing in the audience was also included.
Unable to take his eyes off the blackboard, he couldn’t help but mutter under his breath, “Disproof? It’s actually the proof by contradiction method?! Impossible. I also tried it previously…
“That’s it… I understand now… I see…”
Zhou Xuan and Wang Ziyi, seated next to him, exchanged a bewildered glance.
Sitting in the back row, Zheng Xueqian gulped. He was so nervous that he was about to break his pen.
It was not to cheer Cloud Hao on, but rather, he didn’t expect this guy, who slept diagonally across from him, to be so awesome!
I made a mistake…
Zhu Kening and Liang Ziyuan didn’t have any unusual reactions, though. One was not interested at all, while the other couldn’t understand it. They just thought that it seemed kind of incredible.
The entire class of 1801 and 1802 was dead silent.
Whether it was a top student or an underachieving one, all of them were stunned as they stared at the processes written on the blackboard.
Cloud Hao didn’t pay any attention to the expressions of the people behind him. He was wholly focused on the blackboard, feeling himself entering an unprecedented state.
How should he explain this?
It was as if the whole world had slowed down.
Only his thoughts continued to accelerate…
Is it because of the [Mathematics Proficient]?
So this is the effect of the quantitative change bringing about qualitative change…
Although his intuition told him that this accelerated thinking process could be even faster. It could be further developed until it finally reached the so-called “God” domain! However, for him at this moment, even this extent of acceleration was more than enough.
What was placed before him was nothing but a question that he had done before. It was far from creation.
A trace of understanding gradually rose in his heart.
At this moment, Cloud Hao finally understood a little about what kind of existence this so-called Expert system was.
Time ticked by on the wall clock.
When the second hand had made almost three turns, Cloud Hao stopped moving the chalk in his hand. He turned his head to look at Old Li standing next to him.
“…I’m done.”
He didn’t know if Professor Li Xuesong had heard him, as he didn’t react. His eyebrows didn’t even move.
In order to verify that this old man wasn’t asleep, Cloud Hao asked politely, “Is there anything wrong with the steps?”
Professor Li Xuesong finally snapped out of his reverie.
He stared straight at Cloud Hao, then looked at the blackboard. After which, he moved his stiff neck, as if shaking his head yet also nodding, and uttered, “There’s nothing wrong…”
As soon as he heard these words, the stone suspended in Cloud Hao’s heart finally fell on the ground.
As expected of River Town University.
It truly is quite impressive!
In his previous life, this had been an examination question to stress people out in the IMO competition. In this life, it was actually a critical-thinking question for the first advanced mathematics lesson.
A wave of pressure arose in him. Cloud Hao was too embarrassed to ask the professor if he really didn’t need to come anymore. After uttering an “I’ll head back down then”, he quietly snuck off the lectern.
There was pin-drop silence in the classroom.
Nobody knew who started it, but applause rang out.
Sitting back down on his chair with his eyes wide open, He Ping mumbled something indiscernible.
On the other side, CLoud Hao went back to the last row and sat down. He always had the feeling that there were a lot of people around him watching him. This also made him feel uncomfortable for a while. After all, he always had a low sense of existence.
Fortunately, the applause only lasted for a short while.
As Professor Li Xuesong returned to the lectern without saying a word, the students in the classroom also re-focussed and attentively stared at the blackboard. They were prepared to listen to the lesson.
“The answer is the same as what has been written by this classmate. It’s basically a model answer… You guys copy it down. If you don’t have time to write it down, take a picture. If you don’t understand something, ask him. I won’t go into the specific details.”
“Next, turn to page 12. We’ll continue from where we left off in the previous lesson…”
Professor Li Xuesong seemed to have been dealt some kind of blow. In the second half of the class, he unexpectedly didn’t nag about those “young people nowadays”, “the men from the old calendar were like this and that”, and other incomprehensible things, which he usually did.
However, Cloud Hao didn’t know if it was his misperception or something else, but he felt that the professor seemed somewhat distracted.
Or rather, preoccupied.
When he thought about this, Cloud Hao couldn’t help but be a little worried. Did my lateness infuriate him?
But it shouldn’t be?
To err is human. Besides, I was just late, and I’ve already acknowledged my mistake. My attitude is definitely proper! If he’s still angry, that’s really petty, isn’t it?
There was also Zheng Xueqian…
This guy kept turning his head around to look at him during the lesson, making Cloud Hao feel oddly embarrassed.
The bell between classes finally rang.
Without a word, Professor Li Xuesong left the advanced mathematics book behind and walked off.
Everyone thought that he had gone to answer nature’s call, but they didn’t expect that after five minutes, when the bell signaling the start of class rang, it was a young Ph.D. male student who came instead.
Looking at their similar hairstyles, they were certain that he was Professor Li’s student.
Sure enough, his opening remarks confirmed everyone’s conjecture.
“Professor Li Xuesong has something on. I’ll be teaching you in the second half of the class.”
The Ph.D. student smiled as he looked at the adorable freshmen and picked up the textbook on the lectern. He then scratched the back of his head and said, “Uh, the professor left in a hurry just now…
“Who can stand up and tell me where he left?”