The school goddess, she becomes more and more beautiful

Chapter 216 Finale

Mingcheng No. [-] Middle School, Song Ranran.

The little girl who got full marks in the first league test.

As the president of the Provincial Mathematics Association, he still has a strong impression of her.

As early as the first exam, although he was not present to invigilate the exam at that time, the name Song Ranran was mentioned several times verbally by the teachers in the later marking session.

The handwriting is beautiful, the problem-solving process is perfect, the answers are all correct, and an answer sheet is like a work of art.

I just don't know if the performance of this retest will be equally eye-catching...

The chairman expressed his expectation.

Song Ranran, whose attention was all attracted by the question, didn't notice that there was a person standing behind her. She quickly deduced the idea of ​​solving the problem in her mind, and the tip of the black marker pen rubbed against the manuscript paper to make a rustling sound, and lines of mathematical formulas were written out.After realizing that the direction of her thinking was correct, her eyes lightened slightly, and she immediately jumped to the next step.

The invigilator looked beside her for a while, and nodded with a slight arc of his jaw.

But immediately, the satisfaction in his eyes gradually subsided, and he felt a little uncomfortable.

Song Ranran's progress in solving the problem is not slow, and even the calculation is very fast. Occasionally, there is a deviation in thinking, and he can quickly turn back after the experiment——

At least, this is a bit beyond the chairman's estimate.

These four questions in this year's exam were carefully selected and prepared for these students.

He destroyed a lot of brain cells when he wrote the questions, and it was the turn of this group of students to solve the questions, and they had to be treated like "beating".

The chief examiner stared at Song Ranran's answer sheet with an unpredictable expression for a while.But he couldn't stand still, and walked back and forth again, secretly making some judgments about the performance of the other students.

Fortunately, not all candidates went as smoothly as Song Ranran.

Occasionally, a few students made a "reserved version of scratching their ears and scratching their heads", and the president of the Mathematics Association thought it was quite interesting.

During the exam, the invigilator should not disturb the students too much.

The president also grasped the measure, observing was observing, but he never made a sound, and kept a certain distance from the students. After going down for two laps, he returned to sit on the stage.

About an hour before the end of the exam, Song Ranran did the last question.

Generally speaking, the difficulty of the questions that can be the finale on the paper is by no means ordinary.

Of course, sometimes the solution to the final question may not be so difficult, but the requirements for thinking are absolutely high.

Candidates need to find a perfect idea in the limited time in the examination room. It is undeniable that the difficulty is doubled.

Song Ranran stretched out her hand and rubbed her slightly aching temple, adjusted her mentality and lowered her head to look at the question.

This final question continues the minimalist style of the paper, and the title is only two lines long.

This is a proof question.

Suppose the positive integers a and b satisfy (a+b) divided by (ab+1) equal to k (k belongs to N), and prove that K is the square of a certain positive integer.

There are not many words in the title, but the girl's eyes glanced over it over and over again, trying to find some inspiration.

Are there any theorems related to it?

Have you encountered similar problems before?

Or... in reverse?

……

His thoughts gradually sank, as if everything had calmed down.

Song Ranran closed her eyes and simulated the next few ideas, then opened her eyes and tried to verify it on paper.

Before I knew it, nearly half an hour had passed.

There is not much time left for the exam.

Finally, the corners of Song Ranran's lips hooked slightly.

In the trial and error just now, she finally found a relatively uncomplicated solution that can be proved perfectly.

The most practical is undoubtedly the method of proof by contradiction.

Assuming that k is not the square of some positive integer, then a is not equal to b, consider the indeterminate equation a-kab+(bk)=0.

If a=b, then there is (2-k)a=k, and k=1 is derived, which contradicts the assumption.

……

In the last 3 minutes before the end of the exam, Song Ranran stopped writing.

The sun shines in from the window, and the light shrouds the black hair, making the girl look like a pearl.

　President of the Mathematics Association: I spent so many brain cells to solve the problem, I have to see the effect~
　　Candidate: Bad old man is very bad.

　　In terms of questions, Zhaozhao went to check some of the finale questions of the Olympiad competitions in history, such as the one mentioned in the article. Those who are interested can try it by themselves. Zhaozhao will not describe the problem-solving process in detail here.

　　In fact, sometimes the solution to such competition questions may not be so difficult, but it is undeniable that the difficulty is doubled if you have to find the perfect idea in the limited time in the examination room.Whether it is an exam or a competition, the psychological quality must be stable and don't panic.

　　
　
(End of this chapter)