Enter the Immortal Cultivation

"Demon Emperor Taiyi has a cow grazing in Fusang. Its color is divided into four parts, black, white, brown and yellow, and there are also male and female. When counting the cows, the number of white cows is the number of brown cows plus half of the black cows, plus half of the black cows. The number of black oxen is one third. The number of black oxen is one fourth of the number of yellow oxen, plus one fifth of the number of yellow oxen, plus the number of brown oxen is white. The number of cows is one-sixth, plus one-seventh of the number of white cows, plus the number of brown cows. Regarding the number of bulls, the number of white cows is one-third of the number of black cows, plus another. The number of black oxen is one-fourth the number of yellow oxen, and the number of brown oxen is one-sixth the number of white oxen. Add one-seventh of the number of white bulls. What is the number of the demon king's bulls? Another question is, if the array of black and white bulls is exactly a square, the array of brown and yellow bulls can be a triangle. Also, what is the number of the black and white bulls? What’s the difference between brown and yellow, male and female?”

After Zhilong slowly reported the problem, he looked at Wang Qi with a little pride. When he saw the stunned expression on Wang Qi's face, he became a little worried.

He is very optimistic about this descendant, not only because he has waited for fifty thousand years for such a suitable successor, but also because Wang Qi owns several inheritances and divine rings of mathematics.

This is fate, a wonderful fate.

What if he can't answer? Do you want to give a hint?

When Master Zhilong thought this way, Wang Qi only felt absurd.

Is this...an eternal mystery?

Well, this is indeed a difficult question. Archimedes' herd of cattle problem, a difficult problem that the great mathematician Archimedes had studied for a long time but could not solve.

but. No matter how difficult the problem is, it is time-limited. Before the invention of calculus, the only way to measure irregular shapes was to use the tap-and-fill method, which was extremely troublesome and inaccurate. However, after the advent of calculus, such world problems became just general exercises. Going back to earlier times, there was an era when the Yuan Changing Method was not born. Systems of equations in two variables are difficult problems that can make great mathematicians scratch their heads. There was once a mathematician on earth who resented another mathematician for secretly learning how to solve a system of equations and went to the Inquisition to falsely accuse the other mathematician of being a wizard.

The advancement of mathematical tools and tools for seeking truth has gradually reduced the difficulty of difficult problems in the past.

The reason why primary school Mathematical Olympiads can stump university teachers is that such questions often restrict mathematical tools. Equations and calculus are not allowed, which turns a simple question into a difficult problem.

"The biggest part of this question is the amount of calculation..." Wang Qi sighed and reported the answer directly: "This question has infinite solutions. The minimum solution for the first question is 5916837175686 heads. The minimum solution for the second question is more than two digits. There are more than 16,500 people. It would take several hours to report the answers verbally, senior, let’s just use written ones..."

"Impossible! This is impossible!" Zhilong looked horrified, as if he had seen the most incredible thing in the world.

He was...he actually...he actually gave the answer directly?

"Someone must have asked this question in the past 50,000 years. Did you memorize it by force?" Zhilong found an excuse and forced himself to calm down. But Wang Qi felt that the other party was somewhat fierce and jealous. He listed a few equations on the ground: "So that real people know that in recent times, our Wanfamen Li Sect has made another breakthrough. We have obtained a new learning, named 'Tianyuan Formula', which is based on the elementary algebra of ancient mathematicians, but goes further. …”

Zhilong asked doubtfully: "Elementary algebra?"

"That is, the algebra developed by medieval mathematicians is different from the new algebra developed by our Wanfamen predecessors generation after generation, which is called elementary. By the way, Lian Zong also absorbed this aspect." Wang Qi continued to explain. : "Here we can list a four-element Tianyuan group..."

Zhilong felt that things were beyond his expectation. He hurriedly stopped: "Wait a minute, how does Lian Zong absorb the roots of Li Zong?"

Algebra and number theory are closely related, which is naturally the root of departure.

Wang Qi had no choice but to explain: "There were seniors who wanted to unify the Li Zongzong and create a new one. It was called 'Heavenly Position Law'..."

The so-called heaven position method naturally refers to the foundation of heaven position skill, analytical geometry.

Analytic geometry appeared very early, and it was not difficult for Zhilong to understand it. However, precisely because he could understand it, he was even more shocked: "This...unparalleled wonderful method! This is the Tao! This is the Tao!"

Seeing Zhilong Zhenren dancing happily, Wang Qi couldn't bear it anymore. the gap between them. It is not a gap in personal level, but a gap in the development of civilization. Excluding the ancient method period of nearly 50,000 years, the gap between the two is two thousand years of mathematical development history!

If you want to challenge thousands of talents from thousands of schools with your own body, it will be difficult and difficult!

In an instant, Wang Qi listed several systems of linear equations in eight elements. Then the formulas for square numbers and triangle numbers are listed, and two systems of quadratic equations of two variables are solved.

"The heavenly position method is formed according to Euclidean's Five Laws. To calculate the eight-dimensional heavenly element group, there must be eight perpendicular number axes..."

Zhilong was going crazy: "Eight...how is it possible that there are eight straight lines that are perpendicular to each other and intersect at one point?"

"Oh, this is an expansion of Euclidean Taiyu, called 'Xiangyu'. Ordinary space has only three directions, up and down, left and right, and front and back, which are the three phases. And 'Xiangyu' has infinite phases... …”

"What's the use?"

"Well...it's useless on a normal scale, but it's necessary to study the microscopic world or complex systems..."

The more Master Zhilong asked, the crazier his expression became. But when Wang Qi solved this problem, he had calmed down.

This medieval great strategist sighed leisurely: "The next generation is to be feared, the next generation is to be feared!"

"The Yangtze River... ahem, the waves behind the river push the waves in front, and each wave is stronger than the last." Wang Qi said seriously: "This is a slang in my hometown."

Master Zhilong laughed loudly: "What a 'one wave is stronger than one wave'! This sentence is good! So interesting!" Then, he stared at Wang Qi with burning eyes: "I still have a few questions here... No, I’m not testing you. I know I can’t test you anymore. I just want to know if these problems will be solved in the future.”

Wang Qi nodded: "Okay."

"Is it possible to solve the problems of doubling cubes, squaring circles, and trisecting angles purely by using regular drawing methods?"

Rule-based drawing, also known as ruler-and-compass drawing on earth, is simply a method of drawing with compasses and square rulers without scales. Cubic product, that is, finding the sides of a cube so that the volume of the cube is twice that of a given cube; squaring a circle, that is, finding a square so that its area is equal to a given circle; .trisection Angle means dividing any given angle into three equal parts.

Wang Qi shook his head and said: "It's all impossible. First of all, squaring a circle must involve a number, that is, pi, the ratio of the diameter of a circle. And we can use arithmetic to prove that pi is a transcendental number - what is You can ask about transcendental numbers later. In short, let me say one thing first. It is absolutely impossible to make this transcendental number simply using a circular ruler... It is a bit difficult to explain the cubic product. First of all, we have to talk about a few concepts from which this concept comes. Based on the general solution of Gaoxiang Tianyuan formula...this problem can be converted into a group theory problem..."

Galois theory is one of the important theories in group theory.

Zhen Shanzi took more than half a year of courses than Zhilong Zhenzi, but his receptive ability was not as good as that of the medieval mathematician. He just thought this scene was a bit ridiculous.

The promised test seems to have... turned into a lecture?

And the person being tested teaches the person being tested?

This... is so crazy! (To be continued ~^~)

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