Big Shot, Please Have Some Tea

After school in the afternoon, Shen Qi carried a plastic bag of drinks to a small classroom in the experimental building.

Including Shen Qi, twelve students gathered in the classroom. They were the twelve most mathematically talented students at Nangang Second High School, from different grades and classes. There were no girls, only boys.

They were the math competition team of Nangang Second High School's high school division, representing the school's top mathematical level.

It wasn't easy to be selected for this team; anyone who hadn't scored a perfect score in math was automatically disqualified.

There were a total of 28 science classes across the first, second, and third years. Shen Qi was the only one from his second-year class (Class 2) selected for the school's math competition team. Zhang Wanbang had given Shen Qi a recommendation.

"Big shot, please have some tea."

"Big shot, please have some tea."

Shen Qi took out iced red tea, iced green tea, and lemon tea from the plastic bag, handing them out one by one to the other eleven team members.

Shen Qi's father had taught him that in the early stages of integrating into a new environment, no matter how awesome you are, you must remain low-key, observe secretly, understand the situation, and then start showcasing your abilities.

Actually, Shen Qi knew about this mysterious team within the school. Their meeting place was sometimes in the experimental building, sometimes in the library; they had no fixed location and were hard to find.

This morning, Zhang Wanbang had notified Shen Qi to report to the small classroom in the experimental building after school to prepare for the High School Mathematics League this weekend.

This was Shen Qi's first time meeting the main body of the school's math competition team. Being a newcomer, he first offered tea and observed secretly.

"Which grade and class are you from?" a fatty asked, taking the iced red tea from Shen Qi.

Shen Qi replied, "Second year, Class 2, Shen Qi."

"Oh, Shen Qi, from the second year." The fatty looked at the other students and asked them, "You're all from the second year, are you familiar with Shen Qi?"

"Not really," the male students from the second year all shook their heads.

Who among those present hadn't scored a perfect score in math? Shen Qi, who had risen rapidly in the past two months, used to be a slacker. It was normal for them not to be familiar with him.

Shen Qi maintained an awkward yet polite smile, "I'm a newbie, please take care of me, senior brothers and fellow disciples."

"Sit down, Shen Qi," the fat guy gestured for Shen Qi to find a seat and then introduced himself, "My name is Meng Tianqiang, from third year, Class 5. I'm the captain of this team. Welcome to the team, Shen Qi."

"Big shot, please have another bottle of tea," Shen Qi took out a bottle of oolong tea from the bag and handed it to Meng Tianqiang.

"No more, no more, I'm on a diet," Meng Tianqiang waved his hand, refusing.

Shen Qi unscrewed the cap of the oolong tea and drank it himself.

Shen Qi felt that the team didn't reject him, nor did they show particular enthusiasm.

He'd observe more.

Since it was a competition team, there must be a coach.

Shen Qi noticed that the other teammates were engrossed in reading or doing problems. Half an hour passed, and the coach still hadn't appeared.

Could the training method for this math competition team be self-study after gathering?

Shen Qi dared not ask more and continued to observe secretly.

As it approached 7 o'clock, a person entered the small classroom. It was a small old man, thin and slightly hunched.

"Hello, Teacher Cao!"

"Hello, Teacher Cao!"

Meng Tianqiang and the others greeted the old man.

"Hello, Teacher Cao!" Shen Qi chimed in. He didn't recognize the old man, but calling him Teacher Cao wouldn't be wrong.

Although Cao Xin'an was old, his eyes were sharp. He glanced at Shen Qi, "Newcomer? Recommended by Little Zhang?"

"Yes, my name is Shen Qi, from the second year. Please guide me, Teacher Cao." Shen Qi guessed that this Old Man Cao was probably the team's coach. The "Little Zhang" he mentioned must be Zhang Wanbang.

"Mathematics relies on talent and comprehension. What guidance?" Cao Xin'an said indifferently.

Shen Qi fell silent. How could this Old Man Cao's coaching style be exactly the same as Zhang Wanbang's? Was Zhang Wanbang trained by Old Man Cao?

There was a small blackboard at the front of the classroom. Cao Xin'an walked to the blackboard, picked up chalk, and wrote a problem:

"Given that 'a' is the only real root of f(x) = 0, and a > 0, please prove that f(x) is divisible by (x-a); if 'a' is an imaginary root, please prove that f(x) is divisible by (x+a)."

After writing the problem, Cao Xin'an said to Shen Qi, "New student, you have 10 minutes to write out the proof. I'll be outside smoking two cigarettes. If I come back and you haven't finished, please go back where you came from." He then left to smoke outside the classroom.

Life is full of challenges. Teacher Cao was testing his mathematical ability. Shen Qi stood up, ready to solve the problem.

"Shen Qi, we all went through this kind of test when we first joined the team. Those without ability are eliminated," Meng Tianqiang said, like a seasoned veteran.

"I understand, thank you for the reminder, Captain Meng." Shen Qi walked to the small blackboard and picked up the chalk but didn't start writing immediately. He fell into thought.

It was right to fall into thought; the problems posed by Teacher Cao were certainly challenging. Meng Tianqiang stared at Shen Qi's back. This new junior, he's a nice kid and quite clever, but unfortunately, he lacks real strength.

"This question is too simple. Is this the level of our school's math team?" Shen Qi muttered inwardly. It shouldn't be like this. If Little Zhang (Zhang Wanbang) was trained by Old Man Cao, given their styles, they wouldn't set such a low-level test question, would they? If I trained Chen Xiaoting for a while, she could solve this within 10 minutes.

A trap.

This must be a trap.

Life is full of traps.

The world is treacherous.

Five minutes passed, and Shen Qi hadn't written a single mathematical symbol. He stood in front of the blackboard, lost in thought.

A few second-year students in the seats were whispering, "He's from Class 2, right?"

"The overall math level in Class 2 is average, just a little better than Class 3. Teacher Zhang Wanbang teaches both Class 2 and Class 3."

"Even the top students aren't that outstanding. Huang Zikun has the best math grades in their class, but he still can't make it onto the school team."

"This Shen Qi must have emerged recently in Class 2. I seem to have a slight impression, did he get a perfect score on the last midterm exam?"

"Among us, who didn't get a perfect score?"

The other team members stopped their books and practice sheets, gathering around Shen Qi. Their suspicion deepened. How did this guy get into the team?

Just then, Shen Qi suddenly began writing furiously. Swish, swish, swish. Chalk danced between his fingers, mathematical symbols leaped nimbly, and then, following a certain pattern, they formed an offensive formation, launching a fierce offensive of proof against the hypothesis on the blackboard.

The problem Teacher Cao Xin'an had posed was related to Number Theory.

Number Theory is a branch of pure mathematics, with its earliest roots tracing back to Diophantine equations in ancient Greece.

The most famous work by the Greek mathematician Diophantus was "Arithmetica." While studying "Arithmetica," the "King of Amateurs" Fermat once wrote a hypothesis in the margin, adding a note: "This hypothesis must be true. I have a proof, but the margin is too small to write it down."

This is the origin of the famous "Fermat's Last Theorem" in mathematical history, which was only proven true by the British mathematician Wiles in 1995.

Qin Jiushao, one of the four great mathematicians of the Song Dynasty in China, also conducted in-depth research into Number Theory. The "Jiushao Algorithm" recorded in high school math textbooks comes from Qin Jiushao.

The mathematician most widely recognized in the mathematical community for his contributions to Number Theory is Fermat.

Shen Qi was solving the problem using Fermat's method, which was the main reason he had been contemplating for five minutes without writing anything.

Among the three great masters, Diophantus, Qin Jiushao, and Fermat, Shen Qi ultimately chose Fermat.

Before Teacher Cao Xin'an entered the classroom, Shen Qi completed the proof and then returned to his seat.

"To factor x^2 - 1 into two linear factors, first let

x^2 - 1 = (x + a)(x - a)

Multiply out the terms on the right side of the equation.

Then, equate the coefficients of the terms with the same power of x on both sides..."

The other members of the math team stared blankly at the small blackboard, speechless for a long time. What was this newcomer writing? They couldn't understand it!

The captain, Meng Tianqiang, a third-year student, had more experience. He was the first to understand Shen Qi's proof strategy. "So, Shen Qi, you didn't use the Jiushao Algorithm to prove it, but instead introduced a new method of proof. The process of simplifying complexity was refreshing, and the stroke of genius was equating the coefficients of the terms with the same power."

Shen Qi explained, "It's not that new. This method of proof existed in France in the mid-17th century, while the Jiushao Algorithm appeared in the 13th century during the Southern Song Dynasty. In fact, Qin Jiushao began researching Number Theory earlier than Fermat, by 400 years. Perhaps Fermat had read Qin Jiushao's 'Shu Xue Jiu Zhang' (Nine Treatises on Mathematical Studies). From a mathematical perspective, Fermat's theory is more profound. Standing on the shoulders of giants, of course, one can see further."

"Wow, amazing. Shen Qi, you've already self-taught Fermat's Number Theory." Meng Tianqiang's opinion of Shen Qi instantly changed. He said to the second-year students, "Hey, you're all second-years, are you really not familiar with him?"

"We'll get familiar after meeting a few times!"

"We're familiar now."

"Class 2 has always produced talented individuals. Shen Qi is capable, a late bloomer."

"Shen Qi, now that you've joined our team, we have exactly twelve people. All the Gold Saints are assembled!"

"Shen Qi, what's your star sign?"

The few second-year boys immediately became friendly with Shen Qi, like brothers who had been separated for years.

"You guys are too kind, brothers. Let's hang out together from now on." Shen Qi's secret observations had yielded preliminary conclusions: among the people in the classroom, only Meng Tianqiang had a higher math level. The other ten had at most Math Level 2, if they could be rated.

"What's all the noise!"

Suddenly, a sharp reprimand echoed as Teacher Cao Xin'an returned to the classroom.

Everyone fell silent.

Teacher Cao Xin'an walked to the small blackboard and, with just a brief glance, had already made his judgment.

His expression unchanged, Teacher Cao Xin'an looked at Shen Qi and asked, "How far have you self-studied?"

Shen Qi thought for a moment and said, "I read quite a variety of books. If I had to compare, I'd say I've self-studied up to the second half of sophomore year or the first half of junior year."

Knock, knock.

Teacher Cao Xin'an tapped the blackboard. "Shen Qi, self-studying university material is very impressive? You remember this: during the official Math League competition, you are not allowed to use methods that go beyond the scope of high school textbooks. That's equivalent to cheating. What bad habit is this, did Zhang Wanbang teach you?"

"No, no, no, I came up with it myself, all by myself." Shen Qi certainly couldn't let his teacher, Zhang Wanbang, take the blame. If anyone was to blame, it would be the system.

"Arrogant! Correct this!" Teacher Cao Xin'an roared, then left the classroom with his hands behind his back.

Shen Qi looked bewildered. Teacher Cao Xin'an hadn't commented on his proof at all, just yelled a few insults and left. He was even more formidable than Zhang Wanbang. Were all math teachers like this?

"Did I pass Teacher Cao's test, or not? Should I go home or stay?" Shen Qi asked Meng Tianqiang.

Meng Tianqiang chuckled, "Of course, you stay. Teacher Cao already said you're not allowed to use university knowledge to solve problems in the official Math League competition. Congratulations, Shen Qi. On behalf of Nangang Second High School's strongest Math Olympiad team, I extend our warmest welcome! Come on, let's have some applause!"

Clap, clap, clap.

Warm applause erupted in the classroom. All the team members had officially accepted Shen Qi.

"Big brother, please have some tea." A first-year student wearing glasses handed Shen Qi a cup of lemon tea.

"I bought this tea." Shen Qi took the lemon tea.

"I didn't have time to buy new tea, but the ceremony must be observed. Senior Shen Qi, could you teach me Fermat's Number Theory when you have time?" The first-year student looked genuinely eager to learn.