Teacher Xu, Please Take Care of the Reckless Students in Your Class

topic:

设正整数a，b满足ab+1可以整除a^2+b^2，证明（a^2+b^2）/（ab+1）是某个整数的平方。

"what's going on?"

The first time Teacher Fang saw this situation, he was stunned on the spot, "Is that person on the podium a student? Not a teacher, right? Where is the math teacher in their class?"

The group leader is more concerned about the question on the blackboard.

"It's weird! Isn't this the famous Olympiad problem?"

"Because the Olympiad Physics Competition and the Olympiad Mathematics Competition have a lot of connections, and this question was recognized as the most exciting and difficult question in history at that time, it has already been out of the circle, and many people know it."

Teacher Fang, "???"

"This question is a math competition question?"

"It looks very simple, and it's easy to understand! Why is it difficult?"

The team leader said, "The International Mathematical Olympiad is similar to the International Olympiad in Physics. Students come from all over the world. There are 6 questions in total. The competition is divided into two days and three questions are done every day, with a total time of 9 hours."

"The questions are basically proof questions, with 7 points for each question, for a total of 42 points."

“试题大致上会分为简单、中等与困难三个等级，第1与第4题属简单，第2与第5题属中等，第3与第6题属困难。”

"The topics are provided by the participating countries outside the host country, and the host country forms a topic proposal committee to select candidate topics from the submitted topics."

"The national team leaders arrived several days ahead of the team members to discuss the questions and official answers together."

Teacher Fang smiled, "Team leader, you are going too far. What are you doing for me with this popular science?"

Team leader, "Listen to me and continue."

"It is said that there was a super strong team in the Olympiad that year, and it once won the first place in total points in a row."

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"But after that, it was surpassed by other countries for several consecutive years, and the first throne was robbed!"

"Maybe out of revenge, mathematicians in that country came up with this well-designed, extremely difficult problem."

"At that time, the six members of the Olympic Committee could not solve the problem provided by the mathematician, so they had to ask the four best number theory experts in the host country. To solve the problem, it is embarrassing that the experts have not been able to solve the problem after a hard battle."

"So, the issue committee was brave enough to send the question to the International Mathematical Olympiad Committee, but they deliberately added two stars to the question, indicating that it was a very difficult question."

"After deliberating for a long time, the committee really dared to use this question and put it in the competition."

"As expected, this question has indeed broken the record! It has become an International Olympiad problem that no contestant has solved!"

"There is no full score! The highest score is only 5 points!"

"The average score is only points! Chen Heng is the lowest question in the history of the International Mathematical Olympiad!"

"At that time, there were mathematicians abroad, and they were known as one of the most outstanding young mathematicians in the world today."

"He has been a mathematical genius since he was a child. He participated in three International Mathematical Olympiads at the age of 10, 11 and 12, and won the bronze, silver and gold medals respectively. Holder, and later he won a Fields Medal!"

0 .. 0

Not only Teacher Fang, but even Liao Xiaosheng was puzzled.

"Wait! Why did you mention the mathematician?"

The team leader smiled, "Because he participated in the Mathematical Olympiad that year, although he won the gold medal, he only scored 1 point on this question!"

Teacher Fang, "!!!"

Liao Xiaosheng, "!!!"

Only then did they understand that the difficulty of this question is extremely high!

It is not something that ordinary students can solve!

Look at the blackboard again.

Four questions have arisen.

Just when the group leaders were puzzled, the classmate on the podium, namely Wei Minghai, said, "The questions that Teacher Yu left us are these four questions today!"

Questions left by the math teacher in class 30? !

International math Olympiad questions for this group of students? !

Give them the hardest math Olympiad problem ever? !

And looking at the performance of everyone in the class, everyone doesn't know that these questions are math Olympiad questions, and they don't know how difficult they are.

The team leader had to think that the students in Class 30, like Teacher Fang at the beginning, didn't think it was difficult.

Shi Leiluo looked at the question and shouted, "It's not difficult!"

no difficulty?

The team leader and Teacher Fang outside both stared, "???"

"Is this classmate a little overbearing?"

Shi Leiluo said, "I remember that Teacher Xu talked to us about Vedas jumping, using Vedas to jump, isn't this problem solved?"