Chapter 1379 "Counter-Intuitive" Conjecture

The ABC conjecture is not the same as other mathematical conjectures. Its biggest difficulty lies not in the calculation, nor in the abstraction of the proposition itself, but its existence is completely "counter-intuitive".

In simple terms, there are three numbers a, b and c, where c=a+b, if these three numbers are relatively prime, then the d obtained by multiplying the prime factors of these three numbers without repetition looks like d Obviously it will be bigger than c.

For example, just to give an example, a=2, b=7, c=a+b=9, d=2×7×3=42, where d is obviously much larger than c.

However, this statement seems to have nothing wrong with it, but the fact is completely contrary to people's intuition.

There are not only counterexamples, but also many counterexamples.

For example, the ternary array (5, 27, 32), d=30, is obviously smaller than c equal to 32.

Later, mathematicians took a step back and made modifications to the original expression of Joseph Austali, amplifying rad(abc) and replacing it with an r power greater than 1, and also It is the so-called rad(abc)^(1+ε).

That is, when ε is any real number greater than zero, the counterexample of d=rad(abc)^(1+ε)>c exists!

However, the number of these counterexamples is limited!

Since this question was raised, because of its "counter-intuitive" characteristics, it has been the number one problem plaguing the mathematics community.

In the algebraic sense, the interaction between addition and multiplication corresponds to an infinite number of possibilities, so the prime factors of two natural numbers and the prime factors of their sum should have no relationship in mathematics of.

However, the magic of the abc conjecture lies in this.

It connects two unrelated algorithms in the eyes of mathematicians in a magical way, and discusses the mathematical laws between the two.

Even if it seems to be wrong at first glance, no one can disprove it, and even according to the test results of distributed computing, it is very likely to be correct.

Just like countless face-slaps in history, scientific conclusions such as "Newton's Theorem of Inertia" and "Galileo's Leaning Tower of Pisa Experiment", which seemed to violate common sense at the time, were finally successfully verified.

Moreover, after these counter-intuitive theories were confirmed, without exception, they greatly promoted the development of science at that time.

Just like Professor Dorian Goldfeld’s evaluation of it, although the ABC conjecture is not as well-known as Fermat’s last theorem, many members of the public are baffled by why mathematicians study a conclusion that seems to be valid both positive and negative, but because With its unique counter-intuitive properties, its value is no less than Fermat's last theorem.

If this conjecture is confirmed, it will solve many famous Diophantine equation problems in one fell swoop.

And this includes Fermat's last theorem...

After returning from Professor Perelman's side, Lu Zhou went straight back to his office in the number institute.

Compared with the environment at the Jinling Institute for Advanced Study and the Space Launch Center, he still prefers the atmosphere of the Mathematics Academy when studying mathematics problems.

Asking Assistant Zhao to make a cup of coffee, Lu Zhou, who had been sitting in front of the desk for a long time, took out a ballpoint pen from the pen holder, and quietly thought about it with a piece of blank draft paper.

In fact, at this moment, he is not only troubled by purely academic issues.

And about that so-called "holy relic".

Compared with the manned boarding fire office and Chang'an Avenue, he actually knew more inside information.

This is not only because he is the person in charge of the 128 anomaly project, but also because he has seen three memories of the old universe civilization before, and even communicated face-to-face with the observer civilization.

All kinds of clues indicate that the holy relic is probably not an extraterrestrial civilization, at least not the kind of extraterrestrial civilization imagined by other high-level people except him, but a piece sent by the observer civilization to the solar system that is said to be "Something" that can change the fate of the universe.

According to them, it was a gift.

It's just that due to various reasons, just like many errors in the experiment, this gift not only arrived in the solar system billions of years earlier, but also fell on a civilization that had nothing to do with their plan.

If analyzed from this angle, there is no small possibility that it comes from the old universe.

According to the content of the conversation recalled by Dr. Fan Tong, Lu Zhou can even make a bold assumption that the so-called vanished Martian civilization might have been "enlightened" by that thing.

After all, they call it a "holy relic"...

"Is solving the ABC conjecture a prerequisite for dialogue?"

"I originally thought that the first dialogue between human civilization and other civilizations would probably start with the dismantling of large prime numbers, or other questions that are more concise in form..."

"Go straight to the mathematical conjecture, the threshold is too high."

Different from simple and easy-to-understand numbers such as pi and Planck's constant, mathematical conjectures involve not only mathematical laws, but also human mathematicians' understanding of mathematics.

At least in Lu Zhou's view, if it's for communication, it's definitely not the best choice to say hello with mathematical conjectures.

Of course, the premise here is for communication.

If it's purely for "testing", then that's another story.

Perhaps it was his own illusion. After reading the work log of Project 128, Lu Zhou always felt that although this "holy relic" was curious about human civilization, it didn't seem like he really wanted to communicate with them.

What do you say?

At least in his opinion, this topic really has the meaning of "embarrassing people".

Just as Lu Zhou was thinking wildly about the blank draft paper, a string of bubbles suddenly popped up from the lower corner of the laptop placed next to him.

[Master, there is new mail! ()】

New mail?

Thinking about who would send an email to him at this time, Lu Zhou said.

"Help me open it."

The bubbles disappeared.

As the browser opened, the email was quickly presented to Lu Zhou.

The content of the email is very short, even to the extent that the text only has one sentence:

【I've been waiting for you for half a year, so I would like to ask, have you finished dealing with the matter at hand? 】

Signed name——

Satoshi Nakamoto.

Originally, when Lu Zhou saw this letter, he was still a little confused, but when he saw the name of the inscription at the back, he immediately reflected what this email wanted to express.

At the same time, the expression on his face became weird.

Around the end of last year, when I had just completed the 524-qubit computer and the "void theory", this anonymous address with Satoshi Nakamoto's ID sent me an email, saying that I planned to discuss academic issues with myself.

Out of curiosity about the mysterious founder of Bitcoin, I seemed to have promised him at the time that I would send him an email back after finishing the matter at hand.

As a result, he went to Stockholm later, and encountered such exciting things on the way to Copenhagen on the cruise ship, so that he completely forgot about this agreement after returning home.

But to be honest, this is not his pigeon.

After all, he seems to have never finished dealing with the "things at hand"...

Even now.

Looking at the email, Lu Zhou couldn't help but feel a little troubled.

what to do?

Not in the mood to discuss cryptography at all...

By the way, there is nothing to discuss about that stuff.

Just when Lu Zhou was thinking about whether to just goo, he suddenly had an idea and thought of a brilliant idea, so he quickly edited an email by typing on the keyboard.

[...I'm sorry that I didn't reply to your message in time. After returning from Stockholm, too many things kept me from getting away, such as the subject I'm researching at the moment. 】

[Of course, it would be great if you could help me solve this trouble. I promise that whatever you want to discuss, I'll be there for you. 】

This is probably the most tactful refusal.

Lu Zhou smiled embarrassedly. At the end of the email, he typed the abc guess intact, clicked the send button, then closed his laptop, and continued to look at the draft paper on the table. Initiated to stay.

Time passed by every minute and every second.

Just when Lu Zhou had gradually entered the state and almost forgot about this little episode, the screen of his mobile phone flickered suddenly.

[Master, your reply! ()】

reply?

so fast?

Looking at the string of bubbles on the phone screen, Lu Zhou froze for a moment.

Out of curiosity about the content of the reply, he couldn't help turning on the computer again, and logged in to the mailbox through the browser.

Like the previous email, this reply is only one line long.

[I just studied this question, if you are interested, I put the proof method in the attachment. 】

Lu Zhou: "...???"