I was a top student in America.

The next morning.

The national team's intensive training camp officially began in the small lecture hall of the mathematics building.

Because the United States team performed poorly last year, ranking only fifth among all participating countries, the Mathematical Association of America (MAA) has gone all out this year.

For this training camp, MAA not only invited several top university professors as coaches, but also relied entirely on lecture notes compiled by the professors themselves, without using any existing materials or textbooks.

The core focus of the course is to de-emphasize fixed problem-solving routines and emphasize imaginative thinking and broadened perspectives to cope with the unpredictable questions of the IMO (International Mathematical Olympiad).

There was still some time before class started, and the coach hadn't arrived yet.

After settling into his seat, Li Ao took out the thick book on ordinary differential equations from his bag and continued his study.

Ordinary differential equations are essentially a direct continuation and core application of mathematical analysis. With a solid foundation in mathematical and real analysis, and the added benefit of the "learn by analogy" approach, he found it easy to learn and progressed quickly.

[Under intense study conditions... Intelligence +0.1]

【Intelligence: 117.2】

……

Soon, Professor William Carlson, the number theory instructor, walked in with coffee and lecture notes.

He is very young and is an assistant professor at Princeton University. He has published top-tier articles in both analytic number theory and algebraic number theory.

Although this was his first time serving as the coach of the United States national team, he appeared confident and prepared.

He had previously heard other coaches complain that these gifted students often used strange tricks to solve problems in discussion classes, making the coaches feel embarrassed.

But Carlson didn't care.

Ten years ago, he also sat in a similar classroom as a competitor to prepare for the IMO, and he was very familiar with these so-called "unconventional techniques".

"Hello everyone."

Carlsen picked up the chalk and quickly wrote his name and email address on the blackboard. He turned around, dusted off his hands, and said, "From today onwards, I will be teaching number theory. Just call me William. My requirement for everyone is simple: let's bring back six gold medals in the main competition."

As it turns out, those who manage to get a faculty position at Princeton are indeed highly capable.

As the content unfolded, he broke down the difficult theorems in the number theory module into a clear and logical framework.

The classroom quickly quieted down, with only the tapping of chalk on the blackboard remaining, which the students listened to intently.

Except for Li Ao.

He lowered his head slightly, his fingers constantly turning the pages of the lecture notes.

Professor Carlson's pace of instruction was still too slow for him.

After a number theory class ended, during the break, Li Ao closed his book and noticed that his physical attribute had quietly jumped up a little again.

[Stamina: 114.2]

"It seems that the intense mental exertion during this period has also led to a steady increase in physical strength," he thought to himself.

As the get out of class ended, the tension in the classroom eased slightly.

Since the next number theory problem-solving class was still in the same classroom, most people stayed in their seats, eating and chatting.

"Guys," Mike leaned back in his chair, stretched, and started the conversation, "what are your plans after the IMO? How about we get together and go on a trip for a few days?"

Although the training camp has just begun, there are less than two weeks until the IMO main competition.

There is at least a two- or three-week gap between the end of the main competition and the start of the school term.

The relaxed atmosphere fell silent for a few seconds.

Kevin spoke first: "I'm already in 12th grade, and I'll be going straight to college when school starts. I plan to join a research group to do research, so I need to get familiar with the environment beforehand. I won't be able to hang out with you guys."

He was going to MIT, a place teeming with talented people and fiercely competitive. To stand out, wasting time was absolutely not an option.

A two- or three-week vacation is perfect for studying in advance.

Natalia had similar thoughts, and she chimed in, "Although I'm only in 12th grade this semester, I'm planning to find a research group to experience scientific research in advance, and I'll probably spend the rest of my vacation in the library."

After hearing what the two men said, Michael's face fell.

"Damn," he said, scratching his head in frustration, "You guys are pushing yourselves way too hard! You've been busy all summer and you still have to study?"

He sighed, leaning back in his chair with a hint of frustration. "The competition is in Annam this time. I even looked up some travel guides and was thinking of inviting you guys to hike and see the waterfalls at Baima National Park. Well, after hearing what you guys said, I'm starting to get anxious too... Forget it, I'm not going out to have fun. I knew that hanging out with a bunch of lunatics like you would eventually make me assimilated."

He never asked Li Ao, who was standing next to him, because there was no need to.

Everyone knows that this kid enjoys studying every day and wishes he could study 24 hours a day. Expecting him to go out and play during holidays is about as difficult as making Niagara Falls flow backward.

Li Ao listened to their discussion silently without interrupting, but he had already clearly planned out his holiday arrangements in his mind.

Soon, the break ended, and the number theory problem-solving class began.

Professor Carlson returned to the podium with his lecture notes, and without further ado, turned and wrote the title on the blackboard:

"Let p be an odd prime number, and a be an integer relatively prime to p, such that a^(p-1) leaves a remainder of 1 when divided by p^2."

"Proof: For any positive integer n, a^(p^(n-1)(p-1)) divided by p^(n+1) leaves a remainder of 1; further, determine whether the conclusion still holds if p^(n-1) in the exponent is replaced by a smaller positive integer."

After writing the last half of the parentheses, he put down the chalk and turned around: "Look at this number theory problem first. I'll give you ten minutes to think about it. Later, I'll call on some people to come up and prove it using different solutions."

Having been bombarded with summer camp sessions, everyone has become accustomed to this high-pressure mode of "multiple solutions to a problem and public criticism of errors."

As soon as Carlson finished speaking, the classroom was filled with the rustling sound of calculations being done on scratch paper.

In this gap, Professor Carlson habitually paced back and forth along the corridor.

But his gaze always seemed to fall on Li Ao, whether intentionally or unintentionally.

He had noticed it since the last class: the young man was intently flipping through his notes, not paying any attention to the lesson.

Even now that it's time for practice problems, Li Ao is still engrossed in his own progress.

As a coach, Carlson felt it necessary to give the young man a little nudge and make him realize his own situation.

Just ten minutes later, he stopped, his gaze fixed on Li Ao, and he smiled slightly:

"Then Leo, please go first."

Li Ao originally planned to finish all the lecture notes during the problem-solving class so he could save time to continue studying ordinary differential equations, but he didn't expect to be the first one called on.

He paused briefly, then quickly capped his pen and got up to walk toward the blackboard.

As the most eye-catching figure in this national team, his movement immediately drew the attention of the entire class.

Everyone stopped writing, waiting to see what solution he would come up with.