I control the AI ​​empire thanks to the geniuses in my group.

When Zhang Hengyuan brought Su Zhou back to the math teaching and research group office, Teacher Wang had already arrived.

Teacher Wang is in his early fifties and is an external competition coach for Chongming Middle School. It is said that he coached students in the provincial team in his early years, and later went to teach at a university. After retiring, he was invited back by Zhang Hengyuan after three visits to his humble abode.

He was holding an old-fashioned briefcase and was taking out lecture notes from it, stacking them on the table.

"Old Wang, I'd like to change the format for the first class today," Zhang Hengyuan stopped Teacher Wang at the door.

"In what form?"

"Let the students speak."

Teacher Wang paused for a moment, looked up at Zhang Hengyuan, and then at Su Zhou standing behind him.

Which student?

"The first place winner in this selection test is Su Zhou."

Teacher Wang looked Su Zhou up and down, neither saying good nor bad, just grunting in response, stuffing the handouts back into her briefcase, and following them to the classroom.

The news spread very quickly.

When Su Zhou entered the classroom that had been temporarily requisitioned, the other seven people had already arrived.

Zhao Zixuan was still the same as always, sitting casually in the second row with his feet propped up on the back of the seat in front of him, grinning whenever he saw Su Zhou.

Song Yuhan sat by the window, twirling a pen in her hand, her eyes calm.

Chen Feng and Li Minghui were sitting together, and they both saw Su Zhou walk straight toward the podium.

"Wait a minute," Li Minghui spoke first.

He stood up, glanced at Su Zhou on the podium, and then turned to look at Zhang Hengyuan and Teacher Wang who had walked to the back.

"Coach, what does this mean? Are you having Su Zhou teach us?"

Zhang Hengyuan leaned back in his chair, arms crossed, and remained silent.

Li Minghui continued, "I'm about to participate in the Western Mathematics Invitational Competition, and time is already tight. I'm here to get guidance from professional teachers."

He paused for a moment, his wording already quite polite.

Chen Feng hesitated for a moment, then added softly, "Isn't it a little... inappropriate?"

The atmosphere in the classroom became a little awkward.

Zhao Zixuan put his leg down and was about to say something to help Su Zhou out of the predicament when Zhang Hengyuan spoke up.

"Are you done talking?"

Li Minghui shut his mouth.

Zhang Hengyuan stood up from his chair, walked to the aisle in the middle of the classroom, and scanned everyone around him.

"There's a tradition in the field of competition training, I don't know if you're aware of it, that is, having outstanding students give lectures on stage. This is not only a test of their own abilities, but also an inspiration for other students. Almost all the top schools for competitions across the country, such as Hengshui High School and Huazhong Normal University Affiliated High School, have this practice."

"From now on, not only Su Zhou will have to speak, but each of you may be called up by me to speak."

Then he pointed to Su Zhou on the podium.

"In this selection test, Su Zhou ranked first out of eight people. The first place student goes to the first class, is that fair?"

Li Minghui opened his mouth, but didn't refute it further.

Being first in a test is being first in a test; that's a hard and fast result. If you come in second, you have no right to challenge the first place in this matter.

Chen Feng withdrew his gaze expressionlessly, leaned back in his chair, and crossed his arms.

The others didn't say anything more and just looked at Su Zhou.

Su Zhou stood on the podium, facing seven pairs of eyes with different expressions below the stage, thinking to himself that he definitely couldn't talk about the "Zhou-style Secret Manual" during class.

The contents of the notes are not free; each of the eleven students from other schools paid 550 yuan for them, so he can't possibly share them here for free.

So what should we talk about?

Su Zhou glanced at the audience and then did something that surprised everyone.

He closed his notebook and pushed it to a corner of the podium.

"I don't know what level everyone is at right now, so I won't prepare any content in advance," he said. "Just throw up any difficult problem you've encountered recently, and I'll address it on the spot."

Zhao Zixuan almost jumped off his chair.

Dude, are you crazy?

What if someone asks you a question you don't know the answer to? Wouldn't you be completely stumped on the spot?

Even Zhang Hengyuan sat up slightly.

He asked Su Zhou to give a lecture on stage to test Su Zhou's teaching ability, but he didn't expect Su Zhou to choose the hellish difficulty level directly, let others give questions, and solve them on the spot.

This model has only two outcomes: either it makes someone a god or it leads to their demise.

Chen Feng looked at Su Zhou, a slight smile playing on his lips, a mixture of anger and amusement.

He pulled a piece of draft paper from his bag, which was covered with calculations, and at the top was a problem circled in red.

"The final question from last month's Hua Luogeng Gold Cup," Chen Feng pushed his draft paper forward, "the last big question, in the field of number theory."

"I've been trying for two days and haven't been able to make it, and neither has anyone else. Why don't you give it a try?"

Li Minghui and the others nodded in confirmation.

Su Zhou stepped down from the podium and picked up the draft paper.

Suppose that a positive integer n satisfies n≥2 and n divides 3^n + 4^n. Prove that n must be a multiple of 7, and find all values ​​of n≤1000 that satisfy the condition.

Su Zhou didn't speak immediately after reading the question.

Zhang Hengyuan, who was in the back row, also saw the question.

He knows the answer to this question.

The final question of the Hua Cup competition was a standard comprehensive number theory problem, involving divisibility theory, Fermat's Little Theorem, and the concept of order. Its difficulty level was already at its peak for junior high school competitions.

He was about to say, "Su Zhou, could you explain something simpler?", but the next second, Su Zhou had already turned around and walked towards the blackboard.

The chalk fell on the blackboard, making a soft tapping sound.

Su Zhou first wrote a line: Step 1: Modulo 7 analysis.

"If n divides 3^n + 4^n, what is the relationship between n and 3^n + 4^n? It's not immediately obvious."

He spoke as he wrote, not too fast, but every word hit the mark.

So the first step isn't to calculate it by brute force, but to guess.

Zhao Zixuan's eyes widened: Guess?

「n=7的时候，3^7 + 4^7 = 2187+16384=18571，18571÷7=2653，整除。」

Su Zhou glanced back at the audience: "What about when n=14? You can check it yourselves, it's divisible. But when n=2, 3, 4, 5, 6, it's not divisible at all."

"This shows that the number 7 did not appear by chance."

Chen Feng, who had been leaning back in his chair with his arms crossed, could no longer maintain his posture as Su Zhou wrote the third line on the blackboard.

He involuntarily lowered his hand, leaned forward, and stared intently at the blackboard.

"Wait... how did he jump that step?" Chen Feng's brain started working frantically, trying to keep up with Su Zhou's train of thought.

But he discovered with despair that he couldn't keep up.

Not only him, but Li Minghui, who was sitting next to him, was also stunned.

Li Minghui's mouth was slightly open, and the pen he had been twirling in his hand had fallen onto the table with a soft thud, but he was completely unaware of it.

As a top student who was about to represent his school in the Western Mathematics Invitational Competition, he had actually struggled with this problem in private. He spent three whole nights working on it, wasting half a notebook of draft paper, and finally got stuck in a logical dead end.

He thought that even if Su Zhou was incredibly talented, he wouldn't be able to solve a problem of this level.

But what's going on now?

Everyone else was also staring at the blackboard, afraid to lose focus and miss the crucial information.

The back of the classroom.

Although Zhang Hengyuan maintained his coach's authority on the surface, his unconscious swallowing betrayed the turmoil in his heart.

"This kid... the range of his thought processes is terrifying!"

He cursed inwardly. He knew Su Zhouqiang was strong, but he didn't expect the other party to solve problems so quickly.

Teacher Wang, who had never met Su Zhou before, suddenly stood up from his chair when Su Zhou had written half of the blackboard.

Teacher Wang strode to the middle of the aisle, looked at the blackboard, and couldn't help but mutter, "This intuitive approach...it's so beautiful! So decisive!"

After writing on the blackboard, Su Zhou turned around and said, "The answer is that n can take the values ​​7, 14, 21, 28... all the way up to 994, for a total of 142 solutions."

"I've written out the process in as much detail as possible. If you still find this step a bit challenging, I can break it down to the basics. Would you like me to explain it again?"

The audience was silent.