Jiang Shuiyuan does not know that the smallest number that can be expressed as the sum of two regular cubic numbers in n different ways is mathematically called the nth taxi, which is generally written as Ta(n) or Taxicab(n). So far, scientists have only found 6 taxi numbers, of which 2 is the first taxi number, which can be expressed as 1^3+1^3, and only this one way of representation, so it can be written as Ta (1), and 1729 is the second taxi number.

Of course, 1729 is not just the second taxi, it is also the third Zeisel, the third Carmichael, and the 364th Harshad. It's a pity that Jiang Shuiyuan is now more obsessed with Chinese studies, and he changes his way every day to compete with the "Summary of the Four Libraries of the Whole Book", and his familiarity with other subjects is limited to the level of ordinary high school students, so he naturally doesn't know so much.

Ge Juntian pinched the time for a minute, and then clapped his palms: "Sixty seconds is enough for a talented person to find out the wonders from it, and even if a person without talent gives him sixty hours, the final result will still be the same." Okay boys, have the courage to admit the facts, don't be stubborn anymore, and quickly hand in the answers you have written!"

Jiang Shuiyuan was about to get up, but saw that a tall and thin boy had already handed the note to Ge Juntian. Ge Juntian only glanced at it, then nodded approvingly: "Yes, yes, what's your name?"

"Zhang, Zhang Jin. Whether he was too nervous or stuttered himself, he stammered his name.

Ge Juntian asked again, "Do you know what the Carmicel number is?"

"No, I don't know. Zhang Jin replied with a wincing face.

Ge Juntian patted him on the shoulder: "It doesn't matter, you will know later!"

Since someone snatched the soup, Jiang Shuiyuan calmed down instead, and took advantage of Ge Juntian's interval to collect notes one by one and re-examine the magic number 1729. Although it was only for a few seconds, it made him discover another wonderful thing about this number: 1729 = 7×13×19, and 7, 13, and 19 are all prime numbers. He didn't know how many of those numbers would be in the entire range of positive integers, but it was undoubtedly another feature!

As soon as Jiang Shuiyuan finished writing this characteristic, Ge Juntian stretched out his hand and said a little impatiently: "Little handsome guy, you not only have to resist stubbornly, you simply want to fight to the end! It's a pity that talent is not something you can touch by stepping on your feet and stretching out your hand." The entrance to the Temple of the Sun in Delphi is inscribed with the famous phrase: Know thyself, O man. The so-called self-knowledge includes not only recognizing one's own outstanding talents, but also recognizing one's own mediocrity and inability. However, it is obviously far more painful for you high-spirited teenagers to recognize the latter than the former, and it is both a wise decision and a brave analysis to truly recognize your ordinariness and live an ordinary life with a calm heart!"

Jiang Shuiyuan replied coldly: "In other words, you have done a brave analysis and wisely decided to become an ordinary teacher in an ordinary middle school after graduating from college?"

Ge Juntian was suddenly choked and rolled his eyes, and the other classmates also covered their mouths and laughed.

"I hope your talent isn't in words!" Ge Juntian looked a little cold. As the pride of the sky, almost all he heard from childhood to adulthood was praise, although some people scolded him for being perverse, unkempt, and arrogant, but no one dared to deny his talent, because although he was proud, dirty, and crazy, he did have strength and capital. I didn't expect to be despised by a little kid today, how not to make his heart angry?

However, after he glanced at the note a few times, his attitude immediately turned 180 degrees, and he asked eagerly: "Classmate, do you know the number of taxis and the number of Camitchell?"

"What's that?" Jiang Shuiyuan was sure that Ge Juntian was speaking Chinese, and he could hear every character he said, but when they were put together, they didn't know what to do.

Ge Juntian immediately patted his head: "Look at my pig's head! Do you want to know what the number of taxis and the number of Camitchells is, and it is my turn to make irresponsible remarks? I am afraid that I will already become famous and be selected for the junior class of Jingshi University!" Then he sincerely apologized: "I'm sorry, I sincerely apologize to you, please forgive me for my rudeness and rudeness just now! Indeed, talent is not something that you can touch with your feet and stretching out your hand, because it is in your hands!"

"Wow-" The audience suddenly rang out.

Before, Ge Juntian boasted that his talent was rare in the world, and everyone thought that he might not meet one in his life, but he didn't expect that in a blink of an eye, he began to praise someone for being talented, and everyone naturally wanted to look around to see what a talented person looked like.

The senior brother who was helping on the side also showed a shocked look, you must know that not long ago, he had just seen Ge Juntian's arrogance and no one in his eyes, and he had crushed the self-esteem of a group of top math students in the third year of high school into foam. I didn't expect him to apologize to a student so sincerely, what else can he say besides showing that this classmate is talented and terrifying?

Seeing that Ge Juntian's attitude did not seem to be fake, Jiang Shuiyuan did not think much of himself: "Thanks to the teacher's false praise, the student is ashamed." I just hope that you will be more tolerant and generous with your students in the future, and not too harsh. ”

"Yes, yes, yes, you are right, I will definitely change it and encourage it!" Ge Juntian admitted his mistake very simply, and then explained with a smile: "Anyway, we will get along for a long time in the future, and when you stay with me for a long time, you will find that although my mouth stinks, I am still quite easy to get along with! By the way, I haven't asked your honorific name?"

"River water. ”

"Okay, Jiang Shuiyuan, we know each other now!" Ge Juntian patted Jiang Shuiyuan's shoulder with a spring breeze on his face, but turned his face and shouted to the other classmates: "What about your note? If you don't hand it in, it will be invalid!"

The classmates who watched the excitement hurriedly handed over the note in their hands. Ge Juntian threw it around while reading, and read more than ten notes in less than half a minute, and said with an expressionless face: "Except for Jiang Shuiyuan and Zhang Jin, the two classmates stay, everyone else should go back! In the future, you can come to class regularly and do exercises, don't spend too much time on the Olympiad, the gains outweigh the losses." I have time to read more textbooks of other subjects, pay attention to balanced development, and strive to get into a good university in three years!"

The other 18 students couldn't help but look at each other: After working hard to be admitted to the Olympiad Club, could it be that after doing a seemingly child's play test, the dream of winning the award and becoming famous will come to an abrupt end? Among them, Li Zhili, who was tied for first place in the selection examination of the mathematics group of the Olympiad Society, was particularly indignant, because Jiang Shuiyuan had just taken away the first crown of his grade in the previous monthly examination, but he did not expect that he would steal the limelight again, and he couldn't help but ask: "Teacher Ge, may I ask why the two of them can stay, but we have to go back directly?" ”

"Because you are inferior to them!"

Ge Juntian's answer is always so hurtful, invisible, and a fatal blow.

"How are we inferior to them?"

"Yes, a question, a number, a minute, a piece of paper, how can you see that we are inferior to them?"

"We need a reasonable explanation!"

……

More than a dozen students clamored.

Ge Juntian stretched out his hand to stop their arguing: "Since you are going to die, let you die clearly!" As he spoke, he walked to the podium and picked up chalk, and explained while writing the blackboard: "1729 is a very wonderful number in mathematics, because it is not only the Hashad number, but also the Zousel number, the taxi number and the Camitchell number, of course, these concepts are too esoteric for you, but people with a little sense of mathematics should be able to notice that 1729 is equal to 7 times 13 times 19, which is barely a beginner——"

"That's how I broke down the note!" Li Zhili immediately interrupted Ge Juntian's narration.

Ge Juntian sneered: "Breaking down this number, elementary school students can do it, are you proud to do it right? Obviously, normal people will try to decompose it when they get this number, that is, take a certain number to remove." Needless to say, 2, 3, 4, 5, and 6 can be seen at a glance as impossible, and 7 will naturally be removed, and after 247, 2, 3, 4, 5, 6, 8, 9, 10, and 12 are all impossible, so you can only take the three numbers 7, 11, and 13 to try, and the result will be clear at a glance. Isn't this kind of question just a matter of half a minute for senior elementary school students?

"And the question I asked is what is the singularity of the number 1729, in the process of trying to remove it, have you noticed the singularity of the numbers 7, 11, 13, etc.? Just listing 1729 is equal to 7 times 13 times 19, but not noticing that 7, 13, and 19 are all prime numbers, just like buying a lottery ticket and winning 5 million, but you don't pay attention to the prize. Who can be blamed for this? And to be able to notice that these three numbers are prime numbers can only be barely regarded as a bit of a mathematical feeling, and he is a person with a heart. ”

"So, what did he write, write?" Zhang Jin asked stammering, pointing to the source of the river.

Ge Juntian's tone immediately slowed down: "You have all noticed multiplication and division, but the first thing Jiang Shuiyuan noticed was the cube and addition, after he got the number 1729, he keenly found that it can be represented by the sum of two cubes, and there are two expressions, and it is the smallest number that can be represented by these two methods among all positive integers." If you are fortunate enough to be exposed to advanced mathematics in the future, you will know that this type of number has a proper name called 'taxi'. Obviously, Jiang Shuiyuan didn't know what a taxi was, but he was keenly aware of the characteristics of this number, this is talent!"

Then he sincerely exclaimed: "Such a person is a real genius!"

-- This is the 180th vote of the addition, and now Uncle He still owes everyone 210 votes, 240 votes, and 270 votes for three chapters. Uncle He is working hard!!

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