"The skull hurts."

Looking at the dense draft paper in front of him, Su Mu felt powerless for the first time.

Verify that (a2+b2)/ab+1 is the square of a positive integer.

This sentence can be understood even by junior high school students, Su Mu was stunned and couldn't think of any particularly good ideas that could be proved, and at most only half of it could be proven.

Sometimes it feels like you've caught something, but sometimes it's like you can't do anything.

The road to simplicity.

Su Mu even began to believe in the saying "the shorter the topic, the more difficult it is".

"It's only an hour."

Su Mu glanced at the time, because the first two questions also took a lot of time, and he felt that the time was a little insufficient for the first time in the Olympiad competition.

"it."

Su Mu raised his head and wanted to relax his thoughts again, but saw that a student in the examination room had already handed in his papers.

What's the situation??

There was someone who turned in the paper before him.

Su Mu subconsciously wanted to take a look at the situation with his super high eyesight, but he couldn't see clearly because he was too far away and the perspective was too close!

Little by little, time passed.

A cold sweat appeared on his forehead, and he felt that he was still on the tip of the horns.

Another twenty minutes were wasted.

There was only more than half an hour left before the exam, and Su Mu still had no clue.

Rao is his expression is very steady.

I still can't help but make a little wave in my heart.

If he makes a mistake here, the Huaxia team will definitely fall into a disadvantage in terms of team total!!

The Turkish brother next to him has already completed the first two questions, and his progress has caught up with Su Mu, and he is about to start tackling the third question.

Su Mu sighed.

Although he said that if he was given more time, he would definitely be able to demonstrate this topic.

But the reality of the situation no longer allows him to delay!

Relax your wrist a little, then put the pen on the table and close your eyes.

"Ding, you consumed a white skill point and activated the extreme computing skill, the skill duration is five minutes, and it can no longer be used for a natural day."

…

…

Noisy.

Noisy.

Su Mu only felt the voice in his ears buzzing.

There is the sound of the student in front swallowing saliva.

There is the sound of the invigilator moving his steps.

There was the sound of team leaders chatting outside the examination room...

After Su Mu started the limit operation, the whole world department changed its appearance!!

The corners of Su Mu's mouth were slightly raised, unlike the noise of the outside world, he was now in an extremely calm state!

Every tissue in the body, every cell, and even the organelles in every cell, all began to function as hard as they could!!

In his retina, the whole world began to slowly break down into lines, the eyes of the teachers, the reflection of the mirror, and his brain almost included the entire exam room in the calculation!!

Because he had experimented once in the poetry conference before, Su Mu quickly grasped his mind, his time was only five minutes, and he needed to find the solution to this problem in these five minutes.

It can't be said that he started from scratch, after all, in the first two hours, he himself has tried many kinds of releases.

Now using the limit calculation is just to force the tip of the bull's horns.

Look at the topic in front of you.

Su Mudi picked up the pen and calculated on the scratch paper at a strange speed.

It's blazing fast!

Originally, if a pen quickly drew lines on the paper, it would cause a loud noise, but under the control of Su Mu's strange strength, no one noticed his current abnormality!

"It's kind of interesting."

While answering his own questions, the information of other candidates also came to Su Mu's mind one after another.

The Turkish brother's first question has been proven wrong, and most of the students in the entire exam room are working on the third question.

A boy in front of him has a very good idea of solving the problem, and the way of using geometric transformation is also quite a clever method.

To be honest, Su Mu didn't actually plan to copy other people's methods, but this extra information kept entering his mind.

In the blink of an eye, the brain automatically isolates this information.

Su Mu has the confidence to make his own solution, and looking at other people's ideas will delay time.

"1 minute and 12 seconds."

With the addition of limit operation, Su Mu gave a correct argument, which was one of the breakthrough directions selected by Su Mu at the beginning, and the limit operation realized Su Mu's steps on this basis.

If you want to prove that (a2+b2)/ab+1 is the square of some positive integer, you can know that a,b, in the expression (a2+b2)/ab+1 there is symmetry.

Let a a≥b be, and when a=b, there is a positive integer q such that (2a2)/a2+1=q.

(2-q)a2=q, q=1, and a=b=1 satisfies the question.

So, we just need to talk about the cases of A>B.

In this case, only another s and t need to be satisfied, a=bs-t, and s≥2,0≤t

Bring a=bs-t into the equation (a2+b2)/ab+1 and expand.

After a series of deformations, the final conclusion can be reached.

The method of deformation is complicated, and the values of s and t are also a bit cumbersome, but under Su Mu's limit operation, these problems are not a problem.

……

Su Mu was not surprised that he could answer it in such a short time, after all, there were so many ideas paved before, and there were all kinds of information from other players.

However, after calculating it, Su Mu subconsciously did not stop the calculation.

It's not easy to get into this state once, and it can't be said that the remaining minutes are wasted.

He decided to continue the math and see if he could prove it in another way.

"3 minutes and 51 seconds."

Most of the time has passed since the limit operation, and Su Mu successfully calculated the second solution method.

This method belongs to the gradual decline, which also makes use of symmetry.

It's similar to the first one, but a little more concise.

"The third."

Su Mu's mind continued to calculate. I want to try to prove it in a geometric way.

However, after spending more than ten seconds, Su Mu found that the road was blocked.

"Huh?"

Su Mu's expression fluctuated slightly, because while calculating geometry, a very clear solution suddenly appeared in his mind.

This solution is one of the counter-proofs, if (a2+b2)/ab+1=k, then carefully consider the case that k is not a square number.

The solution of this equation (a,b) must not make ab<0, otherwise -ab≥1 will result in a2+b2≤0.

On this basis, in the way of root and coefficient to prove one by one, in the end, the same way, you can also get k must be the square number!!

The last method Su Mu only took twenty seconds to write out the process on scratch paper, but these 20 seconds were far more ingenious than the first four hours!!

PS revised the outline today, and there is only one change

The red envelope has been posted in the group.

In these two days, the school holiday update will be slightly slower.

After the May Day holiday, the update continued.

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