A few minutes ago.

Xiao Ran had already stalled on the last question for six or seven minutes.

He's really in a bit of trouble and hasn't made much progress yet.

However, he was not too anxious, because he only had this one question left, and there were still more than twenty minutes left, which should be enough.

So, he took a deep breath, then closed his eyes and began to think.

It is not difficult to guess the conclusion of this question, but the difficult thing is how to prove it.

Although you can get some points by simply substituting a few numbers and writing a few lines and giving a conclusion, Xiao Ran doesn't want to give up.

Because only if he scores above 140 points in this exam can he be promoted, and in order to ensure the promotion, it is best for him to do all this question.

So, Xiao Ran began to play the Olympiad question bank accumulated in his previous life in his mind, and tried to search for questions that were slightly similar to this question.

But after searching for it, I still don't get much.

The angle of this question seems to be more tricky, and it is different from previous years.

This made Xiao Ran a little dazed for a while, and he didn't think of a good way for the time being.

However, in fact, he can make this question, but he needs to quote the knowledge of the university, but he does not want to use it unless it is absolutely necessary.

Because it's a high school math league after all.

So, Xiao Ran once again performed a simple calculation, he put 1, -1, 2, -2 in first, and made a simple list.

Then line up in several rows.

F(1)+f(-1), f(1)-f(1), f(2)+f(-2), f(2)-f(-2), add or subtract.

A few more lines.

Maybe it's because it's more neatly written this time, and when he saw the numbers that appeared at this time, Xiao Ran suddenly felt a little familiar.

Xiao Ran knew that he must have seen something similar, so he stopped his pen and began to search in his mind to expand the scope.

Finally, this time, he had a catch.

He had a flash of inspiration, and finally understood why he felt déjà vu.

Because two days ago, he flipped through a tutorial book he borrowed while brushing up on the questions, and happened to see a very interesting question once.

And the core of that question seems to be somewhat similar to this question.

Thinking of this, Xiao Ran suddenly became excited, he quickly drafted the paper and calculated, and after a few minutes, he smiled.

There is a door!

With the bottom in his heart, Xiao Ran immediately began to hurry up and continue to write on the test paper.

[Solution:......

Let 24a=k,12b=l,2c=m,12a=n,k,l,m,n are all positive integers,then:......

Therefore, n=3, l=3, k=1, m=11......

Therefore, f(x)=1/24x(x+1)(x+2)(x+3), there must be two consecutive even numbers among the four consecutive integers, and their product energy is divisible by 8.

The product of any three consecutive integers is divisible by 3, and 3 and 8 are coprime, so that f(x) is divisible by 3×8=24.

Therefore, for every integer x, f(x) is an integer.

Certification. 】

After writing the last word, Xiao Ran felt that he had exhausted all his strength.

He glanced up at the time, 10:55.

Seems pretty good!

Hu Jianmin kept looking in Fang Yiyang's direction, and he was now anxious like an ant on a hot pot.

He sincerely hoped that Fang Yiyang could achieve good results.

Maybe his prayer really worked, Hu Jianmin soon saw Fang Yiyang start writing, and soon.

Seeing this, Hu Jianmin was a little relieved, he felt that Fang Yiyang should have a way.

He tried his best to restrain the desire to go over there to take a look, and he never passed, he was afraid that he would disturb Fang Yiyang's hard-won train of thought.

The time came to 10:55.

Hu Jianmin felt that this point in time should be almost over, and he finally couldn't help it.

He first casually looked elsewhere, and sure enough, the last question stumped a lot of people, and they were all scribbling.

After a long time, Hu Jianmin finally came to Fang Yiyang.

He glanced at Fang Yiyang's test paper as if casually, and then his heart was settled.

Because he saw that Fang Yiyang was about to finish the last question.

Then, Hu Jianmin briefly looked at Fang Yiyang's solution idea, which was very good, and it didn't seem like a big problem.

He knew that for a top student like Fang Yiyang, as long as his thinking was correct, nothing else would ever be a big problem.

Hu Jianmin finally put his mind at ease, and by the way, even his mood became relaxed.

He knew that Fang Yiyang was worthy of Fang Yiyang.

As the math ceiling of high school students in the entire Caozhou City, if he can't do it, I'm afraid no one will be able to do it this time.

At this time, the exam was nearing the end, and Hu Jianmin was also ready to return to the podium and wait for the exam to be finished.

But at this moment, he saw Xiao Ran next to him raise his hand, and before he could react, he heard the other party say:

"Hello teacher, I want to hand in the paper!"

Yes!

Hu Jianmin was startled, and only then did he realize that he had forgotten about this Xiao Ran.

He glanced at Xiao Ran's test paper and saw that Xiao Ran had also written the last question full.

He resisted the surprise in his heart and asked with a smile, "Are you done?" ”

"Hmm!"

"No more checks, inspections are over, and it'll be over in two or three minutes." Hu Jianmin then persuaded.

"I'm in a hurry, I have to leave quickly!"

Seeing Xiao Ran's anxious look, Hu Jianmin's heart was full of doubts, what could be more important than the exam.

However, he didn't want to ask much, so he waved his hand and agreed to Xiao Ran.

"Okay, put the test paper scratch paper on the table, pack up your things and go."

Xiao Ran nodded when he heard this, and after packing up his things, Shi Shiran left the No. 8 examination room.

Xiao Ran's early submission naturally attracted the attention of other candidates in the examination room.

Some people were shocked, obviously they didn't expect that someone would submit the paper in advance for such a difficult question.

Some are full of disdain, they think that Xiao Ran is grandstanding and deliberately pretending to be B.

Even Fang Yiyang didn't hand in the papers, they didn't think that this unknown classmate could finish it.

Fang Yiyang also raised his head and glanced at Xiao Ran at this time.

Since Xiao Ran was sitting next to him, he naturally knew that this classmate who left early was still late at first.

He was a little surprised, but he didn't pay much attention to it.

In his opinion, this classmate didn't care about this exam at all, he was just here to have fun.

But he felt that he was different, and he was in awe of every Olympiad exam this time.

Thinking of this, Fang Yiyang retracted his thoughts and continued to check.

Although it was only two or three minutes, he still refused to slack off, let alone think about handing in the paper early.

Because, this time, his goal is not just a province two.

Hu Jianmin looked at Xiao Ran's test paper and was a little dazed.

He has already proctored several Olympiad exams, and in the past, no candidate had ever submitted his papers in advance, even for half a minute.

Even if there are quite a few top students who finish it early, they will check it over and over again until the bell rings.

Because, they know the meaning of time for the Olympiad exam, maybe half a minute will decide their fate.

But this Xiao Ran of Caozhou No. 2 Middle School is too different.

Not to mention being 5 minutes late, I even handed in the paper early.

The most important thing is that he did it all.

What's even more outrageous is that he did it all right!

The final result of those few problems, he and Fang Yiyang did exactly the same.

Hu Jianmin was so shocked that he couldn't speak at this time, he didn't expect that in his examination room, there would be a dark horse that could match Fang Yiyang.

No, looking at it like this, it seems to be a little more powerful than Fang Yiyang!

Thinking of this, Hu Jianmin looked at Fang Yiyang, who was still immersed in checking, and he suddenly became a little worried about Fang Yiyang and Yizhong.

"Ji Shengyu, He Shengliang, Fang Yiyang, you have met a strong opponent this time!"