Yang Ye is pretty good at geometry, and he frowned when he saw this question.
After thinking about it for a long time, I still haven't found a way to prove it. I roughly estimate that it will take an hour and a half at the fastest before I can prove it to a certain extent.
jump over!
Yang Ye made a quick decision and looked at the second question.
Yang Ye: "..."
The second question is actually a number theory question, and it is a very difficult number theory question!
"2. Let P be a prime number. Given P 1 different positive integer, verify: you can take out a pair of numbers from them such that after dividing the larger number of the two by their greatest common divisor, the quotient is
Not less than P 1.”
In Mathematical Olympiad, geometry and number theory have always been among the difficult points. For example, the complicated geometric figure proof question just now made people dizzy, and this question only has a simple sentence, but it takes at least one day.
A whole page of math questions that takes more than an hour to prove is enough to scare countless candidates.
There are many world-class problems related to number theory, and most of them have not been solved, such as the famous "Estimation of Fibonacci Sequences and Bezu Numbers", "NP-Complete Problem", "Hodge's Conjecture", and "Poincaré's Conjecture"
, "Riemann Hypothesis", and "Goldbach's Hypothesis" that almost even non-mathematicians have heard of...
This shows how difficult number theory is.
Of course, this number theory question is not that scary, but it is estimated that 90% of the candidates will be blinded, and even Yang Ye is not confident that he can prove it.
Damn it, is the question writing team of this national competition exam crazy? Didn’t it say that the difficulty of the questions is random? Why are the two consecutive questions at the beginning so difficult? Could they be playing some kind of surprise attack? Qin Ke
I was provoked and the paper was changed temporarily, right?
Yang Ye cursed in his heart, but then he thought about it, how could this be possible? The papers for the national competition were finalized and printed ten days ago...
Yang Ye thought hard for a moment and decided to give up.
Damn it, I got off to a bad start. I wanted to show Qin Ke next to me what the power of a god of learning is, but I didn’t expect to encounter a roadblock at the beginning!
At this moment, out of the corner of his eye, he unexpectedly saw a group of middle-aged and elderly people who looked like experts and professors passing by in the corridor outside the examination room, seemingly heading towards the back door.
Yang Ye couldn't help but take another curious look. Yes, most of these people wore glasses and had a scholarly demeanor. It was not difficult to judge at all.
Moreover, Yang Ye also recognized a well-known mathematics professor from Chenghai City among them, and after hearing about it, he joined the question-writing team for this national competition.
Hey, could it be that the question-writing team came to see how they did?
It's not surprising that Yang Ye thinks this way. He was the runner-up, or second place, in last year's National Mathematical Olympiad. He is also very famous in the National Mathematical Olympiad Organizing Committee.
What's more, when he was taking exams in Chenghai Middle School, teachers often came to watch him do math problems. In the words of the principal, "Watching Yang Ye do math problems made me feel better than after drinking 20-year-old Maotai."
The speed and smoothness with which he solved the problems was described as eye-opening.
Yang Ye is often proud of this.
However... the problem is that in today's national competition, the first two questions are a bit too difficult!
Hearing the gentle and chaotic footsteps approaching from behind, Yang Ye knew that it was the experts and professors approaching, and couldn't help but secretly complain.
I haven't even solved a single question, so how can I show off? I might disappoint these experts and professors.
He flipped through the test paper in a panic to see if the questions on the second page would be easier, but he saw that the seventh question was another geometry question.
And it’s another complex geometric proof question that looks daunting!
Damn it, what happened to the paper this time?
Fortunately, Yang Ye was quick to think and quickly pretended to be "sweeping" the paper calmly and slowly, turning over the paper slowly, as if he was first judging the difficulty of each question.
This will of course result in the loss of the god of learning to a certain extent, but it is better than not being able to do anything at all.
The only thing that comforted him was that while he was flipping through the papers, he quickly glanced at the candidates in front and on the left. He saw that all of them had blue faces and sweat on their foreheads. They were obviously stumped.
Oh, let me tell you, even I can't do it, let alone other candidates.
After taking a sneak peek to the left, he casually glanced to the right as usual, and was surprised to find that Qin Ke had already started writing with a pen.
And it seems that Qin Ke didn’t write it on the draft, but answered it directly in the answer area!
Is there any mistake? This kid found a simple question so quickly and started doing it?
Yang Ye couldn't sit still and couldn't help but want to take a peek at which question he was doing.
Huh?
Although he couldn't see the content of the question clearly, judging from the vague geometric figures, Qin Ke was doing the first question, which he thought was very difficult and time-consuming. The first geometric proof question!
Is Qin Ke crazy? He plans to spend all his time on this first question in this national competition? But even if he is, it is impossible for Qin Ke to come up with the idea of ​​proof in such a short time, right? Even if he is
Focus on this question, and you won’t be able to figure out the entry point of the proof in less than half an hour!
Does this guy not understand at all and is just writing blindly?
While Yang Ye was thinking uneasily, he heard a gasp coming from behind him.
He couldn't help but glance back, and then he realized that five experts and professors were standing behind Qin Ke, watching Qin Ke answer the questions, with shock on their faces.
Hey, aren't the experts here to see me answer questions? Why are they all behind Qin Ke?
And what's going on with their expressions? Qin Ke answered so poorly that experts and professors couldn't bear to look at him?
It's not like that... the expressions of the experts and professors were more like they had seen something incredible and unbelievable.
Could it be that...Qin Ke...has really proven it?
Impossible, impossible, how could a mere bastard student, a guy from a weak province who just sits there and watches the sky, easily solve complex geometry problems that he can't even prove?
No way!
Yang Ye took a deep breath, trying to concentrate on the paper and start doing the questions as soon as possible, but the "rustling" sound coming from Qin Ke's rapid writing on the right seat was so harsh, the sound of writing came from this place in the entire examination room.
, making Yang Ye unable to calm down at all.
Not only him, but also several candidates next to him couldn't help but cast doubtful glances at Qin Ke. However, when they saw several experts and professors standing behind Qin Ke, they immediately looked away in fear.
Even if they have good psychological quality, they feel uncomfortable when they think of several big bosses watching them answer questions from behind.
But Qin Ke didn't seem to notice the gaze behind him at all. The pen in his hand moved like water, and the sound of "sand" fell in everyone's ears, like a storm!
The more Yang Ye forced himself to focus on the question of the test paper, the more he was affected by the "rustling" sound. His heart was in chaos, and countless thoughts were flashing in his mind:
"Is this guy writing blindly?"
"But if I were writing nonsense, those experts and professors would have left long ago, and they wouldn't have such shocked expressions!"
"Did he really come up with the idea of ​​proof after reading the question?"
"But even if he has an idea, how can he write it directly in the answer area without going through the draft calculation? Aren't you afraid of making mistakes and making corrections? If there are too many corrections and it makes marking difficult, points will be deducted! Or even all points will be deducted.
There’s no place to cry!”
He couldn't help it anymore, and peeked towards Qin Ke again, and immediately vaguely saw that the answer area on the left of Qin Ke was full of words. Then Qin Ke stopped and started writing on the right answer area of ​​the first question.
Got up.
Chapter completed!