I was a top student in America.

Professor Philip's familiarity with high school competition problems is in no way inferior to that of a professional competition coach.

He turned around, picked up the chalk, and quickly wrote a classic example problem on the blackboard:

"Let polynomial P(x) be an integer coefficient polynomial, and for any integer m, P(m) is divisible by a prime number p. Prove that the difference P(x+1)-P(x) also satisfies the corresponding fixed factor condition in the modulus p, and give all possible constructions."

After finishing writing, he turned around, dusted off his hands, and said, "Everyone, look at the problem first. This is a very interesting polynomial method problem. Next, I'd like to invite a student to come up and explain their thought process, and then we can discuss it together."

"You should know that being able to solve problems on your own and being able to explain your thought process to others are two completely different things."

Having students answer questions and explain them on the blackboard is a common interactive method in summer camp lectures.

Although the pressure is immense, the training effect is also excellent.

As soon as Professor Philip finished speaking, the atmosphere in the classroom became tense.

Apart from Benjamin and Natalia, a few senior students who were confident in their abilities, everyone else subconsciously lowered their heads, stared at the blackboard, copied down the problems, and started working out the calculations on their scratch paper.

After all, if you stand on the podium and can't write a single word for a long time, not only will you feel embarrassed, but you will also lose points with the professor.

Li Ao, sitting in the back row of the classroom, didn't write anything; he was looking down at a book called Stephen Abbott's *Real Analysis*.

He had already finished reviewing the practice materials for the second phase of the test after he got up in the morning.

As for the question on the blackboard, he glanced at it a few times and had a good idea of ​​what it was, so he simply continued reading his book.

Benjamin, sitting in the front row, was particularly enthusiastic and immediately raised his hand and stood up:

"Professor, may I write down a solution first?"

"Okay, then I'll leave it to you."

Professor Philip nodded and handed over the chalk.

After Benjamin went up to the stage, he not only wrote down the detailed proof steps, but also turned around and explained to the whole class: "This problem mainly tests the construction of finite differences and the uniqueness of interpolation polynomials. The key to solving the problem is to first transform the conditions into difference constants."

As he spoke, his gaze swept in the direction of Li Ao.

Unfortunately, Li Ao kept his head down reading and didn't look at the blackboard at all.

Benjamin felt a little empty inside. He had hoped to use this to provoke Li Ao's fighting spirit and get him to come up on stage and compete, but Li Ao didn't take the bait at all.

With Benjamin taking the lead, the atmosphere in the classroom became much more lively.

Several veteran students, including Natalia and Kevin, also went up one after another, offering different approaches and all of them derived the correct results.

David, the teaching assistant standing to the side, watched the students take turns going on stage, but his eyes kept glancing at Li Ao.

For the past two weeks, he has been busy with his teaching assistant duties during the day and has to stay up late at night to finish his thesis, fearing that Li Ao would finish writing and submit his short paper before him.

If a high school student were to get ahead of him, he would lose face in the research group.

Strangely, even during this algebra lecture today, Li Ao didn't come to him to ask him a single question about paper formatting and writing style.

David was wondering to himself: Has this guy actually started writing anything?

After all, academic papers have very complicated formatting requirements. Even if a high school student with no research experience can derive detailed proof steps, it would be difficult for them to write the correct formatting on their own.

David was pondering this when he heard Professor Philip on the podium suddenly call out a name:

"Leo."

"What's your thought process for this problem? Or what's your opinion on the solution on the blackboard? Come up and explain it to everyone."

The whole class turned around at the same time and looked at Li Ao, who was still flipping through a book in the back row.

Although Li Ao was reading "Real Analysis" just now, he was also distracted by listening to the other people's solutions.

When he heard the professor call his name, he closed his book, stood up, and walked directly to the podium.

It wasn't until he stood in front of the blackboard that Li Ao finally read through the entire question.

He thought for a moment, picked up the chalk, and added a difference expansion next to Benjamin's lines of proof.

Instead of overturning Benjamin's line of thought, he singled out the most crucial step hidden in the middle: first, he wrote P(x+1)-P(x) as the sum of differences of the coefficients, and then, using the condition of the integer coefficient polynomial taking values ​​at consecutive integer points, he proved that this difference also retains a fixed factor in the sense of modulus p.

After finishing writing, he turned around and made two brief summaries.

Although Professor Jensen had mentioned before that this student had strong problem-solving skills, Professor Philip was still somewhat surprised to see the clear logical structure on the blackboard.

"Leo's proof is more concise and the logical structure is clearer."

Professor Philip nodded, his gaze naturally moving across the podium to the thick textbook on Li Ao's desk:

"Were you reading 'Real Analysis' during class just now?"

"Yes, I've finished today's exercises, so I'll look at some other material in advance."

Li Ao answered truthfully.

His tone was calm, but the students below the stage looked at each other in bewilderment after hearing it.

Everyone knows how difficult the exercises in the second phase of the test are and how much calculation is involved.

Being able to finish reviewing before the exam would already be considered highly efficient, but it's only Wednesday now.

Benjamin paused for a moment. He himself was rushing to meet the deadline every day, and he had only completed a little over half of it so far.

How could this kid do it so fast?

Hearing this, David, who was standing to the side, breathed a sigh of relief.

Since Li Ao has been busy doing practice problems and reading real-world analyses these past two days, he probably hasn't had time to write that short essay yet.

No wonder they didn't come to me to ask about the layout.

This way, he can gain a few more weeks to slowly polish his paper.

On the podium, Professor Philip was clearly interested in Li Ao: "Now that you've started learning advanced mathematics, have you joined a research group yet?"

Before Li Ao could answer, he added, "Many masters in the mathematics world achieved results at a very young age. Being exposed to real mathematical problems early on will be a great training opportunity for you."

"If the project is suitable, it can, in turn, improve your current learning efficiency."

"Professor Jensen invited me to join his research group, but I haven't officially started taking on any projects yet," Li Ao replied.

"Well then," Professor Philip said casually, "I happen to have a small project on discrete averages of convex functions. A student of mine only completed half of it, graduating before finishing the part on two-dimensional weights. If you're interested, I can send you the materials to your email later."

"Thank you, Professor." Li Ao nodded.

When he returned to his seat, Benjamin in the row in front of him was sitting there with a stern face, feeling extremely resentful.

I've interacted with Professor Philip the most during these seminars, so why is the professor so enthusiastic towards Li Ao? He even offered him a research topic!

It's worth noting that Benjamin himself had to send several emails to get into Professor Jensen's research group.

He racked his brains but couldn't figure it out.

Li Ao only explained the problem a little more clearly, and his ideas weren't particularly amazing. Why did all the good things fall on his head?

No sooner had Professor Philip left than David approached Li Ao's desk.

Seeing that Li Ao had taken on new work, he couldn't help but "show concern" as a teaching assistant: "You can take your time writing Professor Jensen's short paper, no need to rush. If you encounter any problems with formatting, feel free to come to me, don't be shy. The same goes for Professor Philip's project, don't push yourself too hard all at once."

Li Ao certainly didn't mind asking for advice, but his first draft was indeed finished.

Just this afternoon, he finished re-editing the entire short paper using LaTeX software.

So he replied honestly, "Thank you, Professor David, but I've already finished that short essay and I'm planning to send it to Professor Jensen when I have the chance."

After thinking for a moment, he added, "It's already been formatted using LaTeX."

David's mind went blank when he heard this.

He never expected that this kid would not only finish writing it, but also figure out how to format it himself.

David stood frozen in place for several seconds, his expression somewhat stiff.

He coughed lightly, forced a smile, and patted Li Ao on the shoulder:

"You've finished writing... That's good. Go to Professor Jensen's office before class tomorrow morning. He's usually there around that time."

……