Her research cannot be used by anyone who wants to.
Consciousness directly reaches the deductive space, a new immersive research, is a state of deep research and learning, which allows her to concentrate on her studies and ignite more of the inspiration to help her deduce.
Line after line of equations coalesced beneath Wu Tong's pen, then erupted again, casting a shadow over the rolling lines around him. Gradually, small streams merged into rivers, and the rivers surged to the sea. The joyful sound of breakthroughs resonated in Wu Tong's ears, becoming the drumbeat of victory.
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(4, 127, 131)= log(131)/ log(rad(4·127·131))= log(131)/ log(2·127·131)= 0....
q(3, 125, 128)= log(128)/ log(rad(3·125·128))= log(128)/ log(30)= 1....
For a triple (a, b, c) that satisfies the conditions a, b, c are coprime positive integers and a+b=c, c < rad(abc). In this case,
q(a, b, c) < 1, and the case of q> 1 is rare. In this case, there are high-power small prime numbers among the factors of these numbers.
Three relatively prime positive integers a, b, c, and c=a+b.
The so-called coprime means that their greatest common divisor is 1. Therefore, 8 + 9 = 17 and 5 + 16 = 21 are a group of numbers that meet the conditions, but 6 + 9 = 15 is not.
Then extract the prime factors of abc. For example, the prime factors of 5, 16, and 21 are 5, 2, 3, and 7. The result of multiplying these prime factors is 210, which is much larger than the original three numbers.
For example, 5, 27, and 32 have prime factors of 5, 3, and 2, and the product of their multiplication is 30, which is smaller than 32. But the second case is extremely rare.
If a and b are both less than 100, there are 3044 matching combinations of ABCs, of which only 7 satisfy the second scenario. The ABC conjecture aims to prove that there are only a finite number of matching combinations that satisfy the second scenario.
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Mathematicians denote the product of the prime factors of abc as rad(abc). Let's put this into rigorous mathematical terms today, substituting it into Theorems 1 and 2: We can confidently conclude that for any ε > 0, there exist only a finite number of mutually prime positive integer triplets (a, b, c), c = a + b, such that c > rad(abc)1 + ε.
Thus, the ABC conjecture is proved.
After completing the last two words of proof, Wu Tong stared at the freshly written manuscript. It seemed that the numbers and symbols in her eyes condensed into an increasingly deep light. She did not stop her movements, but materialized a piece of draft paper and continued to write. The reflection in the sky switched to the content of Wu Tong's new writing, which was a leap from number theory to algebraic geometry.
In the gaps between numbers, Wu Tong caught a glimpse of the connection between the arithmetic and analytic properties of Abelian clusters in the algebra he had been studying.
This extends to the BSD conjecture, one of the world's seven biggest problems, whose full name is the Bech and Swinnerton-Dyer conjecture.
Given an Abelian variety over a global domain, it is conjectured that the rank of its Modal group is equal to the zero of its L-function at 1, and the leading coefficient of the Taylor expansion of its L-function at 1 is exactly related by equation to the finite part size, free part volume, period of all prime positions, and sand group of the Modal group.
The first half, often called the weak BSD conjecture, has been solved. The statement of the SD conjecture relies on Moder's theorem: the rational points of an Abelian variety over a global field form a finitely generated commutative group. The precise part relies on the conjecture on the finiteness of sand groups.
For the case of analytic rank 0, Coates, Wiles, Kolyvagin, Rubin, Skinner, Urban and others proved the weak BSD conjecture, and the exact BSD conjecture holds except for 2.
For the case of analytic rank 1, Gross, Zagier et al. proved the weak BSD conjecture, and the exact BSD conjecture holds except for 2 and derivations.
Now the only remaining problem is 2 and the derivation.
Wu Tong did not come out of the state of enlightenment. The proof of the ABC conjecture once again added a lot of accumulated power to the enlightenment stele, which was about to reach the bottom.
Although this power is not enough to help the Enlightenment Stele advance further, it can be used to support Wu Tong's enlightenment state and maintain it for a certain period of time.
Wu Tong is a master in group theory and nearly unrivaled in number theory. Algebra, particularly algebraic varieties, was her first foray into serious research, but it wasn't unfamiliar territory. Having studied mathematics so deeply, Wu Tong can confidently say that no area of mathematics is too unfamiliar to her.
Algebra and geometry were originally her next research priorities, but she suddenly hit upon the idea of working on the ABC conjecture. While studying the proof of the ABC conjecture, she also saw inspiration for the BSD conjecture.
I believe no one would refuse the arrival of inspiration. Wu Tong naturally seized it decisively, followed the direction of inspiration, and began to deduce it urgently.
She started with Fourier series calculations, then extended them with continuous functions from functional analysis, and introduced Langlands program transformation group theory...
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