Kong Jidao was very satisfied with the girl's question and continued with a smile.

"In the 1500 years after discovering the affinity number of 220 and 284, many mathematicians in the world have been committed to exploring affinity numbers. Facing the vast sea of ​​numbers, they are undoubtedly looking for needles in a haystack. Although they have been thinking about generations after generation, some people have even spent their entire lives on this, but they have never gained anything."

"Mathematicians still haven't found the second pair of affinity numbers. In the 16th century, some people thought that there was only this pair of affinity numbers in natural numbers. Some boring people even gave a superstitious color or added a sense of mystery to affinity numbers, and compiled many myths and stories. They also promoted that this pair of affinity numbers have important functions in magic, spells, astrology and divination, and are all nonsense and the great ambassadors of the world."

"After more than 2,500 years after the birth of the first pair of affinity numbers, the wheel of history turned to the seventeenth century. In 1636, Fermat found the second pair of affinity numbers 17,296 and 18,416, and reignited the torch for finding affinity numbers, and found light in the dark. Two years later, the father of analytical geometry, Descartes, also announced on March 31, 1638 that he had found the third pair of affinity numbers 9437056 and 9363584. Fermat and Descartes broke the silence of more than two thousand years in two years, and aroused the waves of the mathematical community looking for affinity numbers again."

"In the years after the seventeenth century, many mathematicians devoted themselves to the ranks of finding new affinities, and they tried to discover the new world with inspiration and boring calculations. However, the ruthless facts made them realize that they had fallen into a mathematical maze. It was impossible for Fermat and Descartes to have a glory."

"Just when mathematicians were really desperate, another thunder broke out on the ground. In 1747, the unparalleled Swiss genius mathematician Euler announced to the world that he found 30 pairs of affinity numbers. Later, he expanded to 60 pairs, not only listing the number table of affinity numbers, but also publishing all calculation processes. Euler is worthy of being the first genius in the mathematics world. His superhuman mathematical thinking solved the difficult problems that were stopped for more than 2,500 years, and was amazed."

"Of course, no matter how great a person is, he will make mistakes and omissions. 120 years passed. In 1867, there was a 16-year-old middle school student in Italy who liked to use his brain and was diligent in calculations. He actually discovered that the omission of the mathematician Euler - a pair of smaller affinities under his eyelids 1184 and 1210 were slipped away. This dramatic discovery made mathematicians fascinated."

Kong Jidao said, looking at Liu Meng with relief, and said loudly: "So, mathematics has never become more and more powerful as you get older. On the contrary, the greatest achievements are founded by young people. Many times, young men are far more powerful than us old guys. At most, old guys only add bricks and tiles."

"If a mathematician has not achieved anything at the age of 30, he will basically be like this in his life. So, what is not the case with the Nobel Prize is that the Fields Medal, the highest prize in mathematics, is only given to people under 40 years old. When he relaxes until he is 40, he has taken all kinds of accidents into consideration. Of course, there are exceptions. Wiles, the final solver of the Fermat theorem, is an accident in an accident. He was not very awesome when he was young, and he was still working hard in his thirties, but he became famous in one fell swoop at the age of 40. We will talk about his story in detail later."

As soon as these words were said, the students around them couldn't help but look at Liu Meng. At this moment, they all felt that Liu Meng was a rare genius in the mathematics world.

It was still the little girl, and asked curiously: "After saying so much, what does Fermat's theorem say? It's not the last theorem known as Fermat's. It is said that even the peerless genius Euler and the prince of mathematics, Gauss, were stumped."

Kong Jidao nodded, looked at the little girl with admiration and said proudly: "To understand the origin of Fermat's theorem, we must first talk about the source of number theory, that is, Diophanto, which is as famous as Euclid. Euclid wrote the "Origin of Geometry" and became a master of geometry. Diophanto wrote the "Arithmetic" and became the pioneering work of number theory and a classic work. The Diophanto equation he proposed made countless descendants fight for it, and there are still a large number of problems that have not been solved."

"Arithmetic is a good book, the "Nine Yin Sutra" in the mathematics community. In the early 17th century, this book was very popular. Mathematics enthusiasts all dreamed of owning one. In 1621, Fermat finally bought this book in Paris. After returning home, he would read it with his time. He conducted in-depth research on the uncertain equations in the book and limited the research on uncertain equations to the range of integers, thus truly starting the mathematical branch of number theory."

"It's just like Wang Chongyang practiced the "Nine Yin True Sutra" to create the Quanzhen Sect." Kong Jidao's leisure time was reading martial arts. In his mind, the mathematics world was just a world of martial arts.

"Everyone knows the Pythagorean theorem, which is the sum of squares of two right-angled sides of a triangle equals the sum of squares of the oblique side. The most classic thing is the sum of squares of the three and four sides. When reading "Arithmetic", Fermat wrote next to the eighth proposition of Volume 11: Dividing a cube number into the sum of two cube numbers, or a four-power into the sum of two four-powers, or generally dividing a power higher than two quadratic powers into the sum of two powers of the same power is impossible. Regarding this, I am sure that I have discovered a wonderful method of proof, but unfortunately the blank space here is too small to write down."

Kong Jidao said this and couldn't help laughing, "It was just such a casual passage. After the old man Ferma died, his son found the relics. From then on, this passage has troubled the wise man of humans for 358 years."

The girl sitting not far away was completely fascinated by the ears and said anxiously: "Didn't Ferma claim to have discovered a wonderful method of proof? Why has it been troubled for so long? Has it been lost?"

Kong Jidao touched his chin and said mysteriously: "In my opinion, I'm afraid it's Fermat's bragging, and he hasn't found a wonderful way of proof at all. Or it's just his brief thinking when reading a book, not thorough and detailed, and he himself doesn't know the difficulty of this conjecture."

"Tsk, are the great mathematicians bragging?" The girl said frankly.

Kong Jidao glared and shouted, "Are mathematicians not humans? If they are humans, they have seven emotions and six desires. Monks eat meat, and Taoists even get married."

The scared little girl stuck out her tongue.

"After Fermat died, there were many mathematical puzzles left behind, but with the progress of human mathematical technology, they were gradually solved. Only the Fermat's theorem named after him has never had an answer. Of course, there were no progress in this process. For example, his contemporaries were thinking, "Didn't Fermat himself brag about it? I said that I have a simple and wonderful way to prove it, but I can't write it here, so I won't write it anymore. Well, you can't write it here. Maybe on the day you are alive, you will write it down there for a while?"

After pausing for a while, Kong Jidao took a sip of beer and said.

"So after his death, many people searched in his manuscript to see if he had left any clues. After searching, they really gained something. Everyone found that Fermat had proved this formula before his death. When 2 became 4, Fermat's theorem was valid. In other words, any positive integer to the 4th power, plus any positive integer to the 4th power, can not be expressed as the 4th power of any positive integer, this has been proved. Well, with such a good start, we will just go down little by little."

"Then, the cruel reality tells us that Fermat's theorem was not that easy. Until 1706, another great mathematician named Euler was born. This is a rare genius who once left behind the famous Euler formula."

"Euler made a little modification to Fermat's method and proved 3. Don't underestimate 3 and 4. Although it is just these two numbers, if you prove 3, you can prove 9th power. If you prove 4th power, you can prove 16th power. So in the group of positive integers, there are actually many numbers that have been solved by these two people."

"The rings of time continue to scroll downward, and Gauss, the king of mathematics, appeared. He was born in the 18th century, but the mainstream of life was in the 19th century and died in 1855. He solved countless mathematical problems in his life. His most proud name is to draw a regular 17th yardstick ruler. You can hear this word, what does it mean? If you only give you two tools, one is a compass and the other is a ruler without a scale, just these two things, can you draw a regular 17th yardstick?"

"You know, drawing a regular seventeen-side ruler is a famous mathematical problem. It has stumped Archimedes since ancient Greece. In modern times, Newton did not solve it. Gauss was a talented man, and the math teacher assigned him three questions that night. The first two questions were easily solved. This question was a little more difficult, so he only used it for one night and solved it. When he solved it, he didn't know that Newton had never solved it."

"Gauss's work influences every field of mathematics, but it is strange that he has never published an article discussing the Great Theorem of Fermatus. In one letter, he even expressed his contempt for the problem. Gauss' friend, German astronomer Obers, once wrote to him, persuading him to compete for the awards set by the Paris Academy of Sciences for the explanation of the Great Theorem of Fermatus."

"Two weeks later, Gauss replied: I'm very grateful for telling me about the prize in Paris. But I think Fermat's Theorem as an isolated proposition had little interest to me, because I could easily write many of these propositions that people can neither prove them nor deny them."

"Maybe Gauss had tried this question in the past but failed. His answer to Obers is just an example of intellectual sour grapes. In fact, if there is any progress in Fermat's theorem, Gauss will come over to see what's going on? So it means that Fermat's theorem is a big problem that makes experts like Gauss hesitate and embarrassed." (To be continued...)

ps: I wanted to write this paragraph a long time ago, but I didn’t expect it to be so difficult to write it, keep it interesting and make things clear.
Chapter completed!