rpbooks Chapter 25 Diophantus' Equation
Chapter 25 Diophantus' Equation
"Well then, without further ado, let's begin."
Professor Hu turned around, his wrist flicked, and he wrote a daunting title and a series of complex mathematical formulas on a huge blackboard.
[Number Theory - Existence of Solutions to Diophantine Equations]
Holy crap?!
A barely perceptible sound of traditional Chinese music suddenly filled the classroom!
Today is the first day!
This is what they're doing right off the bat?!
Is this supposed to be the first thing we're supposed to talk about?!
Swish!
Swish!
The classroom was instantly filled only with the sound of chalk frantically moving across the blackboard and the scraping of dozens of pen tips almost tearing the paper!
All the geniuses were on high alert, their eyes wide open, taking notes with utmost concentration.
At the same time, brain cells are burning furiously, trying to digest those profound derivations that make you want to bang your head against the wall.
Pan Xun completely abandoned his previous nonchalant attitude, his forehead beaded with sweat, and his expression became extremely serious.
While the pen dances across the paper, the brain must also keep a firm grip on the professor's line of thought and logic.
In the brief moment between turning the page, he inadvertently glanced to the side.
"Um? 』
Pan Xun's eyes suddenly bulged out.
Su Hao was staring blankly at the blackboard.
Although the notebook was open, it was a blank page, even cleaner than his face.
He didn't even have a pen in his hand; he seemed to be in a dazed, absent-minded state.
"Ha, even if you're some kind of overrated genius, you're still just a primary school student!"
Pan Xun shook his head.
"Faced with such a high-level concept, at the university doctoral level, you're probably stunned, aren't you?! You can't even hold a pen anymore!"
Pan Xun sneered and quickly looked away.
The proof he was facing was incredibly difficult, and he had no time to pay attention to anyone else.
If he misses a glance, the numbers on the blackboard might immediately form a shape that mocks him!
however.
Su Hao was definitely not listening.
Because he was thinking about something else entirely.
Why did the professor use such a troublesome and cumbersome method?
The moment Professor Hu wrote down the first Diophantine equation, an extremely concise, elegant, and seemingly illogical proof had already taken shape in his mind.
"Using such basic number theory to deduce this is as inefficient as digging a subway tunnel with a spoon."
The meticulous and complex derivation process, which seemed like a miracle to everyone else, appeared to Su Hao as full of unnecessary redundancy and tedium.
"Forcing a solution is too stupid. If we directly introduce elliptic functions as the starting point, three lines of formulas can solve this simple problem in no time."
Watching the professor writing furiously on the podium, Su Hao sighed listlessly, his thoughts drifting far away.
After an unknown amount of time, the final, crisp sound of chalk falling to the ground echoed across the blackboard.
Professor Hu turned around and looked at a group of students below the stage, their faces pale and drenched in sweat.
"Okay, that's it. This is the classic approach to solving this type of equation."
Professor Hu's tone carried a hint of scrutiny.
"Does anyone have any questions? Or is there anything you're struggling to follow?"
The classroom was deathly silent.
You could hear a pin drop!
No one had time to speak.
Everyone is still desperately trying to process the overwhelming amount of information in the questions.
At this moment, Professor Hu's gaze landed precisely on Su Hao.
He was the only student in the room who wasn't taking notes and even had his hands in his pockets.
Among this group of test-taking geniuses who practically wanted to devour the blackboard, he stood out like a searchlight in the dark!
"Su Hao?"
Suddenly called out, Su Hao snapped out of his rant about "digging the subway with a spoon".
"exist."
"I see you haven't made a single note."
Professor Hu narrowed his eyes slightly, his tone revealing neither joy nor anger.
"Have you encountered any difficulties?"
Swish-!
Most of the people present had only heard of Su Hao's reputation for "overpowering opponents of higher levels" in rumors, and this was the first time they had seen him in person.
In an instant, countless complex gazes, including those of suspicion, contempt, and schadenfreude, rained down on Su Hao like a barrage of arrows.
Su Hao was at a loss for words.
He opened his mouth, looked at the derivation written on four full pages of the blackboard, and then at Professor Hu's slightly scrutinizing eyes, appearing somewhat hesitant.
He was flustered, not because he couldn't understand.
Rather, it was because he didn't know how to use the most tactful words to tell him, without shattering the old professor's academic dignity:
What you've been writing for so long is absolutely rubbish!
Su Hao's eyes wavered slightly.
It was a gaze from dozens of eyes, a gaze that carried an almost tangible sense of oppression.
In the huge lecture hall, even the sound of air moving could be clearly heard. Everyone was staring intently at him, waiting for his response.
However, today is only the first day of winter camp.
From childhood, his parents, fearing that his extraordinary talent might lead to a distorted personality, almost pathologically instilled in him the rules of "politeness, consideration, and respect for teachers."
Therefore, he decided to approach the topic by following the professor's line of thought.
Su Hao quickly scanned the blackboard with his eyes.
The four giant blackboards pieced together are densely covered with a massive number of formulas that could trigger trypophobia on the spot.
"Diophantine equations." This was his favorite area.
Around the third century AD, Diophantus, a mathematician from Alexandria, systematically explored various equations with integer solutions in his book "Arithmetica".
These brilliant formulas were once forgotten in the long river of history, until they were rediscovered by modern mathematical giants such as Fermat, Euler, and Gauss, and hung in the sky of the mathematical world.
Su Hao's gaze darted rapidly across the blackboard.
Let's start with the underlying definition in the upper left corner of the first blackboard.
The most basic framework of Diophantine equations, the Pei Shu equation, can be applied instantly.
A sweeping glance extends the Euclidean algorithm.
The brain reconstructed the entire algorithm in a second, and the inverse calculation process was also completed in a brain simulation.
My gaze shifted to the second blackboard.
The formula suddenly became grotesque and complex.
Represented as an integer sum of two squares, Fermat's theorem of squares unfolds rapidly in my mind.
The gaze continued downwards.
Fermat's Last Theorem and Euler's infinite descent method intertwine to awaken and verify every logical anchor point.
I noticed the expansion method used by Professor Hu.
"Hmm, if we directly apply Jacobi's triple product theorem here, it would actually be a bit simpler..."
From the first blackboard to here, a process that would make an average math major pull their hair out, Su Hao only took a few seconds.
"Um? 』
Suddenly, the previously smooth formula reading experience came to an abrupt halt, like driving a Ferrari at high speed on Mount Akina when the front wheels slammed into a reinforced concrete barrier!
Su Hao's gaze was fixed on him.
Near the top of the third blackboard, in the middle of an extremely complex unfolding pattern.
The symbol is misspelled.
That position shouldn't be a '+' sign; it must be a '-' sign.
In the Euler partition function expansion using the pentagonal number theorem, the sign must be changed for this broken formula to hold true!
If you don't change the symbols, won't this thing just explode on the spot?!