On the 25th, the Anhui Province Mathematical Society finally issued an official notice about the league.

The Provincial Mathematical Association needs each city to finalize and send them the list of students participating in the league, so that the next work can be arranged.

Therefore, it is understandable that the announcement about the league was not released until the 25th.

The notice states that on October 12th, teachers who lead teams based on middle schools need to report to Room 16-11 of the School of Mathematics, Research Management Building, East Campus of HKUST.

However, participating students do not need to go to the registration location on this day.

Each student participating in the league needs to bring his or her ID card and a recent two-inch photo, and also pay an entry fee of 50 yuan to receive the admission ticket.

The specific time for the league exam is October 13th, which is Sunday.

The first test will be held from 8:00 to 9:20 in the morning and lasts for 80 minutes.

After the first test, there will be a 20-minute break, and then the second test will take place from 9:40 to 12:10, lasting 150 minutes.

The first test includes 8 fill-in-the-blank questions and 3 answer questions. Each fill-in-the-blank question is worth 8 points, and the three answer questions are worth 16 points, 20 points, and 20 points respectively, for a total score of 120 points.

The second test includes 4 to answer questions, involving plane geometry, algebra, number theory, and combination. The first two questions are 40 points each, and the last two questions are 50 points each, with a full score of 180 points.

If you are a student who has not had much contact with competitions, you may feel a little strange about this arrangement.

Why is it that the first test has 11 questions and the test time is only 80 minutes, and the second test only has four questions, but the test time is nearly twice as long as the first test, with 150 minutes?

This arrangement is naturally because the difficulty of the second test is much higher than that of the first test.

The scope of knowledge involved in the first test will not exceed the teaching requirements and content stipulated in the "Mathematics Teaching Syllabus for Full-time Senior High Schools" of the Ministry of Education in 2000. In other words, the scope of the test is not much different from that of the preliminary test.

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However, the second test involves four aspects: plane geometry, algebra, number theory, and combination. It is in line with the National Mathematical Olympiad (Winter Camp) and the International Mathematical Olympiad. Compared with the first test, it adds some content beyond the syllabus.

Therefore, although it only has four questions, the difficulty of each question is not comparable to the questions in the first test.

As for the final league results, the Provincial Mathematics Association will notify the municipal education bureaus two weeks after the exam ends.

If candidates have any questions about their scores, they can contact the teachers at the Provincial Mathematical Society through the municipal teaching and research staff to review the test papers within two days after the Education Bureau receives the scores.

The final assessment of the provincial first, second and third prizes is based on the results of the two National Mathematics League exams.

The number of first prize winners is determined by the National Mathematical Society, the second prize is determined by 35% of the number of participants, and the third prize is determined by 50% of the number of participants.

Zhao Xiancai also saw this information in the group.

Not long after the Provincial Mathematical Society released this document titled "Notice on Holding the 2013 National High School Mathematics League in Anhui Province", Lin Guangqiang sent it to the competition group of Chengxian No. 1 Middle School.

All students can see it.

On the night when this notice was released, Lin Guangqiang talked to Zhao Xiancai and others about their subsequent trip to Luzhou.

“The examination location for this league is the same as in previous years, it is still held in Luzhou No. 1 Middle School.

Last year, I led the team from Chengxian No. 1 Middle School to participate in the math league. However, last year there was only one student from Chengxian No. 1 Middle School participating in the math league. This year, there were four more students.

Don't worry about your jokes, I have never brought so many people to participate in the National High School Mathematics League.

We will take the earliest bus to Luzhou on the morning of the 12th, and we will arrive at the hotel we booked near the University of Science and Technology at about 11 o'clock. Bring your ID cards and photos. If you don't have any photos, we will take them tomorrow..."

After talking to Zhao Xiancai and others about the league, Lin Guangqiang continued to explain the content of the second trial of the league.

During the time between returning from Yixiu City and the announcement of the league by the Provincial Mathematical Society, Zhao Xiancai had already purchased all the mathematics competition information books and some competition coaching videos he wanted to buy through his class teacher Fang Qiu.

Now Lin Guangqiang is giving lectures above, and Zhao Xiancai is writing questions below without disturbing each other.

"Zheng Wenyi, where did you get this question? Why don't you even have an answer?

There are already enough questions in the competition information books we bought. If you can understand all the questions in them, you don’t need to find any more questions to solve."

During the break, Zheng Wenyi asked Lin Guangqiang a question.

After Lin Guangqiang finished reading this question, he didn't even figure out how to solve it when the school bell rang, so he had to say this.

Since even Teacher Lin couldn't solve it, they had no choice but to look for Zhao Xiancai.

After Zhao Xiancai was answering questions when Zheng Wenyi patted him on the shoulder, he knew that they must have some problem, otherwise they would not bother him.

So Zhao Xiancai also put down the pen in his hand and looked at Zheng Wenyi.

Zheng Wenyi also tacitly handed a piece of draft paper with a title in her hand to Zhao Xiancai.

“Suppose the positive integers a and b satisfy (a2 b2)/(ab 1)=k∈N, prove that k is the square of a certain positive integer.

So this is the question, where did you get this question from?"

After reading the question, Zhao Xiancai seemed to have done the same question, and he asked him curiously.

"This is what I saw in a math competition group I joined before." Zheng Wenyi said.

The math competition group she mentioned was not a group from Chengxian No. 1 Middle School, but was added through the forum.

"You've done this question before, right? Is there any question in the world that you haven't done before?"

Ji Xinglei on the side heard Zhao Xiancai's tone, it seemed that he had done the question Zheng Wenyi asked before, and he was also very surprised and asked.

"Oh, I have indeed done this question, but I actually regret that I came into contact with this question too early.

This question is actually quite legendary. It was the 6th question of IMO in 1988.

That year's IMO was held in Australia. After this question was submitted to Australian four-digit theory experts, no one on the main examination committee solved the question within the stipulated time.

On the contrary, in the IMO examination room, 11 contestants obtained perfect scores.

When I first came across this question, I didn't know how to do it. I only learned it after looking at the answer.

Now if I encounter a similar problem again, I will definitely be able to solve it.

And I think if I encounter a number theory problem of this difficulty again, I will definitely be able to do it.

But questions of this difficulty are hard to come across.

Having said so much, I haven’t solved your problem yet.

The answer I looked at at that time used proof by contradiction.

Although I later thought of some other solutions, I have to say that the method of proof by contradiction is the most classic, and I will use this solution to solve this problem.

First assume that k is not the square of a positive integer and consider the indefinite equation..."
Chapter completed!