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1、Topics of LecturesZengyong LiangI have two topics of Lectures to choose from:1. Exploration on The Proof of Goldbach ConjectureGoldbach conjecture was put forward by Goldbach in 1742. For more than a hundred years, no one can solve it.There are two main ways to solve Goldbach conjecture:1) "a +

2、 b" method:In 1920, brown of Norway proved "9 + 9".In 1966, Chen Jingrun of China proved "1 + 2. Since then, there has been no progress in the "a + b" method.2) Exception set method: it is proved that all even numbers except even number 2 can be expressed as the sum of

3、two prime numbers. So far, most scholars have not proved that the product formula is correct.Since I published the " " in 2009, after more than ten years of efforts, I finally found a comprehensive and perfect solution to Goldbach conjecture through a variety of proof methods from differen

4、t angles and means. This paper introduces the possibility of proving Goldbach conjecture by using the continued product formula.1) (n) The function formula can calculate the lower limit of prime number and prime pair number, which can be derived from the inclusion exclusion formula, Euler function a

5、nd the sieve of Eratosthenes. Namely(n)=n(1) .From (n) ,w (n) function formula for calculating the lower limit of the number of prime pairs can be derived. Asw(n)=(1)The number of prime pairs D (N) derived from the formula of continuous product function is greater than , which proves Goldbach conjec

6、ture. In addition, the geometric figure is used to represent the integer, and the mapping relationship between the internal angle of circle and sector and the number of integers is used to successfully prove the correctness of Goldbach conjecture This paper analyzes the error of the continued produc

7、t function formula, and how to correctly define and deal with it, so that it will only produce a small negative error, so as to ensure that the calculation result is the lower limit of prime number and prime pair number, and meet the requirements of proving Goldbach conjecture.2) The paper provides

8、computer data and trend chart to prove that the function formula is correct. At the same time, it can also provide a large amount of computer related data.3) The second Goldbach conjecture using geometry proves that using a circle to represent the integers in 0,2n, using the mapping relationship bet

9、ween the fan-shaped internal angle in the circle and the component of the number of integers, and successfully using morphological mathematics to prove the correctness of Goldbach conjecture and continuous product formula. The paper also proves that the generation mechanism of prime pairs is basical

10、ly the same from the generation mechanism of prime numbers, and reveals the essence of Goldbach conjecture.At the same time, it provides a new and useful mathematical morphological analysis method and theory to solve mathematical problems in number theory .4) This method solves the proof of infinite

11、 twin prime number at the same time.2. Solutions of Higher order Indefinite EquationsBach and Swinton Dale conjecture is one of the seven "Millennium Prize Problems" proposed by clay Institute of mathematics. This paper will introduce the solutions of various types of high-order indefinite

12、 equations to prove that such equations can also be solved by algebraic methods using structural mathematics.These include:1) a2 + b2= c2 general solution of indefinite equation.2) Proof of Fermat's last theorem: an + bn= cn indefinite equation has no integer solution.3) The proof of Bials conje

13、cture: ax + by= cz type equation has solutions with common factors.4) ax + by+ cy = du solution of multivariate indefinite equations. 5) kax + hby= jcz solution of coefficient band indefinite equations.Through the solution of the above equation, it is proved that the higher-order indefinite equation

14、 can be solved by algebraic coefficient and exponential matching method. Answers the questions raised by Behr and swenton Dale conjecture.The main papers participated in mathematics conferences and published include:In 2009, the paper "Any Even Number Not Less Than 6Can be Expressed as the Sum

15、or Difference of Two Primes" won the "scientific and Technological Innovation Award" of the second national folk science and technology development seminar.Zengyong Liang,( 2010), Any Even Number Not Less Than 6Can be Expressed as the Sum or Difference of Two Primes , Journal of intel

16、ligence. （July 2010）。Zengyong Liang,( 2013), A Practical New Method for Proving the Four-color Theorem, Journal of mathematics learning and Research. (Issue 19 of 2013）。Zengyong Liang,( 2013), No Odd Perfect Number, Journal of mathematics learning and Research. (March 2013).In 2013, he participated

17、in the 5th International Symposium on graph theory and combinatorial algorithm (Tongliao, Inner Mongolia) and made a speech on Hadwinger conjecture (Lectures).Zengyong Liang,( 2016),The Final Pproof of the Four-color Theorem , Journal of Examination Weekly (No. 84, 2016).Zengyong Liang,( 2018), Rigo

18、rous Proof of Goldbach's Conjecture ,Journal of science, technology and Economics (may 2018).In 2018, Rigorous Proof of Goldbach's Conjecture (Lectures)participated in the 2018 International Symposium on Discrete Mathematics and computer mathematics.Zengyong Liang,( 2018), Rigorous Proof of

19、Goldbach's Conjecture, Journal of Applied Mathematics and Physics , /journal/paperinformation.aspx?paperid=87140Zengyong Liang,( 2019),Proof of Beal Conjecture, Journal of Advances in Pure Mathematics, /journal/paperinformation.aspx?paperid=92539,https:/ww

20、/journal/paperinformation.aspx?paperid=92539Zengyong Liang,( 2019),Solutions of Indefinite Equations, Journal of Advances in Pure Mathematics, /journal/paperinformation.aspx?paperid=102965Zengyong Liang,( 2022), A New Method to Prove Goldbachs Conjecture ,Journal of Advances in Pure Mathematics, /journal/paperinformation.aspx?paperid=114833In addition, it can also provide several topics I have solved recently:1） Warings problem: using the modular method and structural mathematics, it is proved that g (2) = 4, g