"Ding, you used a green skill point, reached math level 7, and the current score is 0/1e"

"Ding, you used a green skill point, math level 8, current score 0/10e"

After completing the first question, Su Mu let go of his thoughts and rested on the table for five minutes.

In the second question, he decisively raised his math to grade 8.

It is enough to make a shaft once, and Su Mu has already experienced the difficulty of mathematics.

Now he just wants to reconcile with himself and the world as soon as possible, and there is actually some luck in making the first question before, and he doesn't want to stay up for another hour or two on the second question.

Originally, skill points were saved for the Olympiad competition.

If you keep it and don't use it, it's too sandy.

Question 2.

Let's call an array p=(a,b,c) a Pythagorean array if a,b,c are positive integers and a2+b2=c2. Given two Pythagorean arrays p,q, it is proved that there are positive integers n and the Pythagorean arrays p0,p1,,pn, satisfying p0=p,pn=q, and that the arrays pi and pi+1 have common elements.

The second question is also a short question, and it is a proof question, and the type belongs to the variant of the Pythagorean array.

I don't know if it's because of the fact that mathematics has been upgraded to level eight, or if this problem is really simpler, Su Mu saw the idea at first.

The Pythagorean array, also known as the Pythagorean triple, has been discussed since the time of Babylon, combining mathematics with graphics.

If you want to prove that there are common elements, you only need to prove that the shapes intersect or connect.

"If there is a Pythagorean array p,q,p contains a, q contains b, and pq has an A.D. element, first connect the vertices ab.

"Due to"

"It is only necessary to prove that for any positive integer a≥3, a and a positive integer less than or equal to a and greater than or equal to 3 are connected"

"When looking at a=k, in the Pythagorean array"

"Let k=2r+1, since (2r+1,2r2+2r,2r2+2r+1) is a Pythagorean array, solid"

"It can be proved from the graph that k and 9 are connected, and there are positive integers n and the Pythagorean array p0,p1,,pn, which satisfies p0=p,pn=q, and the arrays pi and pi+1 have common elements"

The second question Su Mu only took less than 20 minutes to complete, and his thinking was clear.

The combination of graphics + mathematics can prove the problem very clearly.

Immediately after that, he carried out the argument of the third question in one go.

The third question is a geometric proof question, proving the tangency of a triangle and a circle, geometry has always been Su Mu's strong point, and his pressure is not very great.

However, since it is the finale, there is still a certain degree of difficulty.

Some arguments had to be written in detail, and various equals and tangents had to be considered, and it took more than half an hour for Su Mu to complete the details.

Finally, after checking twice, Su Mu added the details of the answers to each question, and there was about an hour before the end of the exam, Su Mu handed in the test papers in advance and left the examination room.

There is a classroom next to the exam room dedicated to the rest area.

When he walked out, Su Mu's eyes narrowed.

He found that there were already seven or eight students in the lounge area by this time.

Because it's November, the weather is getting colder.

Although it was indoors, because the air conditioner was not turned on, Su Mu still shrunk his neck.

knew that it was so cold, so he put on the scarf that Yan Xiaoke gave him.

The gold content of the mathematics national competition is obviously much higher than that of the biology national competition, and judging from the seven or eight students who submitted their papers one hour earlier, there are probably not a few real bigwigs.

Before the official end of the exam, the students were not allowed to leave the rest area and use electronic devices, Su Mu looked around and found a place to sit at the back of the classroom.

A male teacher among the teachers in the rest area is sitting on the podium with a thermos cup and watching a TV series leisurely.

The other students didn't seem to know each other, and sat very scattered, some in a daze, and some continued to calculate something.

This made Su Mu a little incomprehensible, since he wanted to continue the calculation, why did he have to hand in the papers.

The bigwigs are really capricious, so it's hard to change the environment and change the mood.

The closest to Su Mu was a chubby boy, probably because he had to wait too long, and he was indeed a little bored, so he looked at Su Mu.

"Classmate, which school are you from?" The chubby boy showed a good-natured smile, and at a certain moment, he really looked like a certain famous comedy star in China. "I'm Chengdu No. 4 Middle School, Yue Hao"

"Yue Hao?"

Su Mu was stunned, and when he heard this name, he suddenly felt even more like, but it was a pity that he couldn't speak cross talk, otherwise he could come with him for a while.

"Su Mu, from Eastern Zhejiang Province."

"Zhedong? In recent years, the Olympiad results in eastern Zhejiang Province have been very good, so it seems that he must be a big guy. Yue Hao said with a smile.

"You handed in the paper before me, you must be stronger than me, I'm here to make up the number this time."

Su Mu sighed, if it weren't for the fact that mathematics had been promoted to level eight, he really wouldn't have the confidence to say that he could hand in the paper in advance.

"That's not easy to say, I can't pass the exam this time." Yue Hao sighed, "I feel that I am going to be cold in this national competition, you bigwigs all said that they came to make up the number, but as soon as the results came out, they were tsk." ”

Su Mu shrugged his shoulders.

Ended this commercial blow.

He did come to make up the number of skill points, so he didn't dare to compliment Yue Hao's coldness.

Really cool people.

I'm afraid I'm still in the exam room full of men doing questions.

"But one thing to say, it's really easy to try this time."

"I feel that the second test will definitely be very difficult, otherwise there will be no way to open the gap in the national competition."

Yue Hao turned his head and changed his words.

directly confirms Su Mu's point of view.

I feel that this level of topics can't open up the gap, this Yue Hao, I'm afraid it's really not a simple character.

Su Mu wanted to say something, but his eyes looked at the door of the classroom.

A few more people walked into the lounge one after another, and one of them was Dai Binbin.

Dai Binbin walked straight to Su Mu's side and sat down, and asked.

"288 and minus 512?"

"Hmm." Su Mu nodded.

Dai Binbin breathed a sigh of relief.

"It feels like there are no particularly difficult questions in this try, and it's easier than I imagined."

Su Mu ""

Su Mu originally thought that after the eighth level of mathematics, he could invisibly pretend to be forced once.

The next time I meet Fan Ze, I can talk a few more words.

But after hearing Dai Binbin and Yue Hao, Su Mu felt that there was no atmosphere of pretending to be forced at all.

Although Su Mu himself thinks so.

But when I heard two people say that the topic is very simple, I still feel a little inconsistent!

This is the Olympiad National Championship!!

Don't you want to lose face in the national competition??

。