Before returning to the college entrance examination, I became popular in the science circle

Her research is not something anyone can use if they want to.

The consciousness reaches directly into the derivation space, and the new immersive research is a state of enlightenment that ignites the derivation assistance on the basis of in-depth study and learning, allowing her to concentrate without distraction.

Lines of calculation formulas condensed under Wu Tong's pen, and then exploded again, reflecting the rolling lines around Wu Tong. Gradually, the streams merged into rivers, and the rivers rushed to the sea.The joyful sound of breakthrough sounded in Wu Tong's ears and became the drumbeat of victory.

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(4, 127, 131)= log(131)/ log(rad(4·127·131))= log(131)/ log(2·127·131)= 0.46820
q(3, 125, 128)= log(128)/log(rad(3·125·128))= log(128)/log(30)= 1.426565
For the triplet (a, b, c) that generally satisfies a, b, c as relatively prime positive integers and a+b=c, c < rad(abc), at this time,
q(a, b, c) < 1, and the case of q> 1 is rare. At this time, there are high powers of small prime numbers in the factors of these numbers.

Three relatively prime positive integers a, b, c, and c=a+b.

The so-called co-prime means that their greatest common divisor is 1.Therefore, 8 + 9 = 17 and 5 + 16 = 21 are eligible numbers, but 6 + 9 = 15 is not.

接着把abc的质因数都提取出来，比如5、16、21的质因数是5、2、3、7，这些质因数相乘的结果为210，这个数比原来的三个数大得多。

又比如5、27、32，它们的质因数是5、3、2，相乘结果为30，就比32小。但第二种情形极为罕见。

If a and b are both numbers less than 100, 3044 abc combinations that meet the conditions can be found here, of which only 7 groups meet the second scenario.What the abc conjecture wants to prove is that there are only a limited number of abc combinations that meet the second situation.

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Mathematicians write the product of prime factors of abc as rad(abc).To express it today in rigorous mathematical language, substitute Theorem 1 and Theorem 2: We can be sure that for any ε>0, there are only a finite number of triples (a, b, c) of coprime positive integers, c = a + b, such that: c > rad(abc)1+ε.

From this, the ABC conjecture was proved.

After completing the last two words of proof, staring at the newly written manuscript, Wu Tong seemed to have numbers and symbols that condensed into a deeper and deeper light in Wu Tong's eyes. Her hand did not stop moving, but manifested He took out a piece of scratch paper and continued writing. The reflection in the sky switched to what Wu Tong was writing, which was a leap from number theory to algebraic geometry.

From the gaps in numbers, Wu Tong got a glimpse of the algebra he had been studying, and a glimpse of the connection between the arithmetic properties and analytic properties of Abelian varieties.

This extends to the world's seven major problems, the full name of which is the BSD conjecture of Behe ​​and Svenaton-Dyer.

Given an Abelian variety over a global field, it is conjectured that the rank of its Modal group is equal to the zero order of its L function at 1, and that the leading coefficient of the Taylor expansion of its L function at 1 is the same as that of the Modal group There is an exact equational relationship between finite part size, free part volume, period of all prime sites, and sand clusters.

The first half is often called the weak BSD conjecture, which has been solved. The statement of the SD conjecture relies on Modal's theorem: the rational points of the Abelian variety on the overall domain form a finitely generated commutative group.The precise part depends on the conjecture about the finite nature of the sand population.

For the case where the analytical rank is 0, Coates, Wiles, Kolyvagin, Rubin, Skinner, Urban and others proved the weak BSD conjecture, and the accurate BSD conjecture is true 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 derivatives
The only remaining puzzle now is 2 and the derivative.

Wu Tong has not escaped from the Qi Fu state, and the proof of the ABC conjecture has once again added a lot of power accumulation to the continued power of the Enlightenment Monument that is about to bottom out.

Although this power is not enough to help the Enlightenment Monument go further, it can be used to support Wu Tong's enlightenment state for a certain period of time.

Wu Tong is skilled in group theory, and almost unrivaled in number theory.Algebra, especially algebraic varieties, is her first time to study major topics, but it is not an unfamiliar field to her. After studying mathematics in depth, Wu Tong can confidently say that there is no field that is too unfamiliar to her in mathematics.

Algebra and geometry were the next key issues she planned to study, but she suddenly had an idea and made the ABC conjecture.On the basis of studying the proof of the ABC conjecture, I got a glimpse of the inspiration to move towards the BSD conjecture.

I believe no one would refuse the arrival of inspiration, so Wu Tong naturally grabbed it immediately, followed the direction of inspiration, and began to deduce it urgently.

She made calculations from Fourier series, and then used the continuous function extension of functional analysis to intervene in the Langlands program to transform group theory...
The so-called Abelian variety is the complete group outline of the geometric whole on the field, which must be projective, smooth and commutative.An algebraic group that is at the same time a complete algebraic variety.

Because she already had a certain foundation, Wu Tong solved the Tate conjecture before Faltings and promoted the idea and calculation method of using Abelian clusters, and found inspiration for the way forward. Although these inspirations did not allow her to immediately solve the BSD conjecture, But Wu Tong can be sure that if she continues along this road, she can reach the end. This is more important than anything else!
Of course, this is without a doubt the most difficult part of it.But Wu Tong still wanted to try to see if he could complete this problem.

She can say that this time, she is not starting from scratch, but making a happy breakthrough in the improvement and optimization section that she is good at.

The Qifu state is very consumption-intensive and the time is limited. Wu Tong almost ran out of energy when he found the direction of the Enlightenment Stone Tablet, and was forced to automatically cut off the Qifu state.

Of course, this actually didn't have much impact on Wu Tong. It was already July.Wu Tong spent two days saving the preliminary paper on the ABC conjecture, and continued to deduce the BSD conjecture.For her, the ABC conjecture that has been broken through is no longer the most critical. The new goal-chasing BSD conjecture is her full focus.

Having found a clear solution, Wu Tong does not have a strong desire for Qifu Space.What she always trusts more is what she has learned. This is not because Wu Tong thinks that she does not need help. No one wants to take shortcuts, but because she understands that help also needs to be based on her sufficient foundation in order to be able to perform at her best. The good effect of adding one to three cannot depend on the enlightenment state.

Wu Tong completed the final proof on the right road at an almost crazy speed.

Substituting this into Modal's theorem and BSD conjecture, it is proved to be true. (End of chapter)