"Forch is one of the Board of Trustees of Oxford University and one of the members of the Russell University Group with 18 decision-making powers. Think about it?"
Xu Heng waved his hand, "Then if my guess is correct, is he also one of the organizers of this Mathematical Olympiad?"
Zhu Tiesen nodded.
Xu Heng immediately shrugged his shoulders, "So... I handed in the paper so much in advance, it's no wonder people aren't curious about it! What's more, I still have a perfect score?"
Zhu Tiesen was speechless for a moment.
Yes!
There is nothing wrong with this understanding!
Although Oxford University, or the Russell University Group has never had a precedent for actively recruiting a certain student, you, Xu Heng, are special!
Your specialness... makes all things possible!
Zhu Tiesen has long stopped treating Xu Heng as a normal situation.
That's why he was worried.
Xu Heng patted Zhu Tiesen on the shoulder, "Professor! Take it easy! There are exams tomorrow and the day after tomorrow! Nobody can tell, right?"
Pfft!
The day after tomorrow?
Little ancestor!
You should do something about Yangjian!
Needless to say?
With your ability here, I'm afraid you will definitely hand in the paper in advance!
In this case, they will only pay more and more attention to you, and the matter will only become more serious...
How do you let me relax?
I should be more nervous!
!!!
Zhu Tiesen looked at Xu Heng, his expression became a little helpless, even his eyes were full of pleading, "Student Xu Heng, can you..."
As soon as he opened his mouth, Xu Heng knew what Zhu Tiesen was going to say.
Xu Heng immediately interrupted Zhu Tiesen, "Professor Zhu, do you know how boring it would be to wait there for a few hours after last night!"
"Besides, I still have a few museums to visit! Please let me go!"
After Xu Heng finished speaking, he ran away quickly.
Zhu Tiesen looked at Xu Heng's back and sighed helplessly, "Hey..."
What can he do?
There was nothing he could do.
After all, he has the final say on Xu Heng's affairs!
But the dazzling Xu Heng, will the Russell University Group miss it?
From Forch's temptations, Zhu Tiesen has already noticed that he is understanding Xu Heng's other talents.
If he knew that Xu Heng's achievements in physics were even higher, then... everything would be even more unimaginable!
This was on the premise that Zhu Tiesen didn't know that Xu Heng helped the space center recover the rocket boosters!
If only I knew!
I am afraid……
"It's dangerous abroad!"
It is too dangerous for a super genius like Xu Heng to be abroad!
"It's just that we can't control student Xu Heng..."
Zhu Tiesen frowned.
In this way, I waited anxiously until the next day's exam.
On the way to Oxford University, Zorro talked and laughed with Xu Heng all the time.
But the question he asked was somewhat targeted.
Xu Heng just smiled slightly, avoiding these topics and not giving him any useful information.
At the same time, Xu Heng turned his gaze to Zhu Tiesen.
Exchanged glances with him.
It was telling Zhu Tiesen that there was something wrong with this guy, let Zhu Tiesen pay more attention.
Arrived at Oxford University.
This exam is divided into six exam rooms.
Each examination room, six people!
And the countries of these six people are not the same.
Today's test paper only has three questions, and the test time is still 4.5 hours, with 7 points for each question!
When the test paper was found, Xu Heng read the questions.
When the exam bell rang.
Xu Heng picked up his pen.
The first question is a graphic proof question:
Let J be the center of the circumscribed circle subtended by vertex A of triangle ABC.
The circumscribed circle is tangent to the side BC at the point M, and tangent to the lines AB and AC at the points K and L respectively.
Lines LM and J intersect at point F, and lines KM and CJ intersect at point G.
Let S be the point of intersection of the straight lines AF and BC, and T the point of intersection of the straight lines AG and BC.
Proof: M is the midpoint of line segment ST.
Without the slightest hesitation, Xu Heng answered.
Answer: Because ∠JFL=∠JBM∠FMB=∠JBM∠CML=12(∠A+∠C)12∠C=12∠A=∠JAL, so the four points A, F, J and L share a circle.
From this, AF⊥FJ can be obtained, and BJ is the angle bisector of ∠ABS, so the angle bisector of triangle ABS coincides with the height, so AB=BS;
In the same way, AC=CT can be obtained.
To sum up, SM=SB+BM=AB+BK=AK=AL=AC+CL=CT+CM=MT, that is, M is the midpoint of line segment ST.
"Hey……"
Take a deep breath.
The examination room was very quiet, and Xu Heng's sigh attracted the attention of the examiners.
They couldn't help looking at Xu Heng.
After all, they found out yesterday that this student got full marks in the preliminaries!
The three examiners looked at each other, and one of them walked gently to Xu Heng's side.
He saw that on Xu Heng's test paper, the answer to the first question had been written!
In an instant, he was not calm anymore, and the corners of his eyes twitched fiercely.
He suddenly raised his head to look at the other two examiners.
Those two frowned, "???"
It seems to be saying: What's going on?
The examiner immediately went to their side and pointed at Xu Heng.
The two approached slowly and walked over...
Just arrived at Xu Heng's side, Xu Heng turned the page and read the second question.
The two were at a loss, "???"
When he came back, he helplessly spread his hands and shrugged.
The examiner asked in a very small voice, "Did you see that? He finished the first question! He even finished the first question!"
"It's only been three minutes since the exam started!"
"I buy it! God! Did he see the standard answer before? How could he do this!"
The other two opened their mouths and looked at the students from the other five countries.
They are still reviewing the questions and haven't started answering them yet!
Three questions, 4.5 hours!
On average, one question takes 1.5 hours!
But Xu Heng, the first question only took 3 minutes!
!!!
The other two examiners were stunned for a moment.
He just turned the page, and when he looked at the second question, he actually finished the first question...
and many more!
The two examiners immediately returned to Xu Heng.
They were staring at Xu Heng!
as predicted!
Xu Heng has already started to answer the second question!
The second question is a proof question:
For a natural number n, if for any integer a, as long as n|a(nth power)-1, there are n2|a(nth power)-1, then n is said to have property P.
(1) Prove that every prime number n has property P; (2) Prove that there are infinitely many composite numbers that also have property P.
This question is not easy for these examiners from the Russell University Group!
But Xu Heng wrote like flowing water.
fast!
quickly!
Non-stop fast!
Prove:
(1) Let n=P be a prime number and p|(a(p power)-1), then (a, p)=1.
因为a(p次方)-1=a(a(p-1次方)-1)+(a-1),由费马小定理p|(a(p-1次方)-1)。
Therefore, p|(a-1), that is, a≡1(modp)...
将这p个同余式加起来即得a(p-1次方)+a(p-2次方)+…+a+1≡0(modp),所以,p2|(a-1)(a(p-1次方)+a(p-2次方)+…+a+1)=a(p次方)-1
Get it!
Look at the second question.
At this time, the three examiners had gathered around Xu Heng.
All of them raised their heads exaggeratedly, couldn't help but stared at Xu Heng.
They thought that Xu Heng would stop and think about the second question!
But people didn't pause at all, just wrote directly.
(2) If n|(a(nth power)-1), then (n, a)=1...
and so……
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