Chen Ming’s approach of using group theory to study Goldbach’s Conjecture really piqued Zhao Yi’s interest.
Group theory is a mathematical thod.
As the na suggests, it is the study of groups, and its importance is mainly reflected in abstract algebra. In abstract algebra, many algebraic structures, including rings, fields, and modules, can be seen as being ford by adding new operations and axioms to groups.
Group theory also plays a very important role in other branches of abstract algebra.
Furthermore, in research in the fields of physics and chemistry, many different physical structures, such as crystal structures and hydrogen atom structures, can be modeled using group theoretic thods. As a result, group theory and its related group representation theory have extensive applications in physics and chemistry research.
However, using group theory for number theory research, especially on pri numbers, sounded very novel.
Pri numbers themselves can be seen as a group.
If group theory could be used to study the concept and properties of pri numbers, it would almost be like unlocking the mysteries of pri numbers.
That is impossible.
So it is understandable that Chen Ming could not continue his research, but the most important thing is the thod and perspective. What kind of thod did he use to connect group theory and pri number research?
Zhao Yi carefully examined Chen Ming’s research content.
Chen Ming did not hesitate to explain his progress to Zhao Yi, as he was inspired by the Riemann Conjecture.
The Riemann Conjecture has a certain number of pri solutions, which are definitely non-continuous, and can be considered as a group.
This is equivalent to dividing the pri numbers.
Chen Ming hoped to categorize all pri numbers into small groups. For example, by designing ten functions whose solutions cover all pri numbers, he would essentially divide the pri numbers into ten sets and study them individually.
Of course.
It was impossible for Chen Ming to consider establishing ten functions. It sounded simple, but it was impossible to achieve in reality.
His research was much more complex, and the thod of dividing pri numbers was also very peculiar. For example, he found three sets of specific pri numbers, and connected them to Goldbach’s Conjecture, proving that the combination of two pairs in the three specific pri number sets could cover all even numbers below ten digits.
This research result had no practical significance because even numbers below ten digits could be decomposed into pri number combinations by computers, which could find not just one, but many sets.
However, without a doubt, Chen Ming’s research approach was very novel.
Zhao Yi couldn’t help but feel amazed, as he had never thought of this approach.
It really was... quite unexpected!
However, Chen Ming’s line of thinking was similar to a proof thod he had previously considered, which was to prove that the combination of pri numbers (including themselves) could cover all even numbers.
As long as it could be proved that the combination of pri numbers could cover all even numbers, Goldbach’s Conjecture would be generally proved.
For example, consider the even number 22.
11 11=22; 3 19=22; 5 17=22.
Three pairs of pri numbers combined equal 22, and there are many, many similar even numbers. In the computable domain, most even numbers can be decomposed into more than one group of pri number combinations.
So, in a broad sense, the content of Goldbach’s Conjecture may be just a manifestation of the property of "pri number pairs covering even numbers."
As long as the overall coverage can be proven in a general sense, Goldbach’s Conjecture will naturally be solved without a fight.
Zhao Yi carefully thought about this and decisively used the "Correlation Law" to try to find out the relationship between the research content in his hands and Goldbach’s Conjecture.
[Usage failed!]
"Failed?"
It was Zhao Yi’s first ti trying a similar thod to obtain the proof conditions for Goldbach’s Conjecture. He was psychologically prepared for failure, but he expected failure due to insufficient energy, not inability to use the ability. "Why is that?"
He then thought about taking out a piece of research content from his bag, which was a proof that there must be a pri number between n and 2n.
[Correlation Law]
[Usage failed!]
"Failed again?"
Zhao Yi frowned tightly, unable to understand why it failed directly and why it couldn’t be used.
In ordinary advanced calculus problems, the "Correlation Law" can be used. Insufficient energy and irrelevance to the problem are understandable reasons for failure, but direct failure ans that the ability cannot be used in proof problems related to Goldbach’s Conjecture.
Subsequently, Zhao Yi continued to ponder this and appeared sowhat listless while talking to others.
In the afternoon, after everyone gathered, they took a car to the capital airport together.
Zhao Yi followed the Science Academy’s team the whole way, always walking beside Chen Ming. He only knew Chen Ming in the team, and although he had seen so of the others, he was not familiar with them.
After getting on the plane, Zhao Yi continued to think while sitting in his seat.
Chen Ming asked with concern, "You seem to be in a daze all the ti. Are you still thinking about the problem of Goldbach’s Conjecture? Or do you have any doubts about my research?"
He hoped it was the latter.
No matter who spent a lot of ti and energy on research, they hoped that their research would be useful.
If he could assist Zhao Yi in his youth, it would be the best proof that he did not waste ti and energy.
Zhao Yi nodded, "I am thinking about your thod and your research, and whether it can be further expanded and applied to the proof of Goldbach’s Conjecture."
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