After handing over the system, the state forced me to study

In fact, this set of test questions is not too difficult, and there are even some questions that can be done by high school candidates.

"Assume a and b are positive integers, and ab divides a?+b?. Prove: a?+b?/ab+1 is a perfect square."

Um?This question?

Isn't this an IMO test question from years ago?

It was almost wiped out at the IMO that year, and even the four number theory experts in the Kangaroo Country at that time failed to make it.

After all, the two ideas of extreme value principle or infinite descending method were not so popular back then, but a lot of similar topics appeared later and were trained badly.

So why is there such a question that seems so simple now?

Lu Xingyao didn't understand.

Forget it, since it's out, let's write it, otherwise it can be so bad.

"First of all, set out the Vedic theorem: Suppose x?, x? is the root of the quadratic equation ax?+bx+c=0, then x?+x?=-b/a and x?x?=c /a

……

Prepare all the 'tools' you need, and then you can start doing the questions.

Proof: If there exist a and b such that c is not a perfect square, then a non-empty set can be constructed..."

I have to say that the principle of good order is really a very magical thing.

"It's time, stop writing."

The teacher in charge of the exam is called Xu Xin. Apart from the usual classes, he was also the leader of the IMO team at the end.

As a teacher with many years of experience, Xu Xin is not unknown in the Olympiad circle.

Following his order, those who were still thinking hard or writing quickly stopped their movements.

However, the pen stopped, but the mouth moved again.

While the people on the stage were still preparing their lecture supplies, there were rustling voices from the audience. Listen carefully, some complained about some of the difficult problems, some were puzzled by the emergence of old problems, and some complained about the old problems. A discussion of solutions to some of these topics.

Even Lu Xingyao was no exception, he was grabbed from front to back and left to participate in the group chat.

"Correct the test paper yourself with a red pen, and collect it after class."

Of course, the specific scoring points will be mentioned during the lecture, one is to facilitate everyone to change the score, and the other is to let everyone understand the scoring points.

"Okay, it seems that there is no need to talk about the first few questions, right? It's so simple, if you still don't know it, just find a tree and kill it." Xu Xin smiled.

The audience laughed together, shook their heads and said, "No."

But, if there are too many people, it is inevitable that there will be a few bolder ones.

No, there was someone who answered quickly: "I want to talk—"

The yelling was so loud that the whole classroom could hear it.

Xu Xin was stunned for a moment, but he wasn't angry either. He obviously knew this person's nature, and it wasn't that he couldn't do it. He just liked to talk ironically in class. His teachers probably annoyed him to death at school.

"Then you go out." Xu Xin pointed to the door.

The class burst into laughter, "Go out."

"There just happened to be a tree at the door, and I went to see God immediately."

……

Lu Xingyao couldn't help but laugh. Watching a play is really fun. These links are his favorite to watch in class.

Who knows, in the next second, extreme joy turns into sorrow.

"Lu Xingyao, what are you laughing at?" Xu Xin looked at Lu Xingyao who was smiling happily.

"Ah?" Lu Xingyao froze.

So many people are laughing, why just click him?

Do you want to target it?I'll report you later.

Lu Xingyao burst into tears in his heart.

The smile on Lu Xingyao's face disappeared, he stood up reluctantly, and said in a muffled voice, "It's nothing."

"Nothing? Nothing, right? Come up." Xu Xin looked serious.

"Huh?" An ominous premonition rose in Lu Xingyao's heart.

When he looked at Xu Xin suspiciously and walked slowly to the podium, he had a premonition.

Xu Xin immediately changed his face and said with a smile: "Come on, come on, this class, we invite Lu Xingyao to give a lecture for everyone, everyone applauds!"

Lu Xingyao's expressionless face immediately collapsed.

He knows it!

hateful!

Xu Xin didn't give him a chance to react, so he walked quickly to Lu Xingyao's seat and sat down. It was just beside the aisle, which was very convenient.

It's just pity for Xu Mingxi who was sitting next to Lu Xingyao, he was trembling and his heart was about to burst out.

It saved a life, sitting with Lu Xingyao is risky.

"Okay, let's start talking. I'll correct your test paper for you." Xu Xin picked up the red pen on Lu Xingyao's desk, and stared at Lu Xingyao, like a student who is eager for knowledge and listens carefully to the class.

Lu Xingyao was under a lot of pressure. Although Guan Lianyi asked him to talk about the topic when he was in school, could it be the same?

First of all, the people sitting below are different.

Secondly, compared with Xu Xin, Guan Lianyi is not ranked at all.

Who is Xu Xin?The person in charge of Guoji has many years of experience in leading IMO teams, and his research in the Olympiad is also ranked among the top three in the country.

So, sometimes, people can't laugh too happily.

How happy I was laughing just now, how sad it is now.

Lu Xingyao took a deep breath, and he could only speak according to his own thoughts and ideas. If what he said was wrong, then wait for Xu Xin to add it below. Anyway, it's okay for him to stand on stage and embarrass himself.

"Let's look at the fourth question first..."