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Old 2020-07-04, 08:40   #23
Jun 2020

22·3 Posts
Default New function, new criterion, new theorem and new conjecture for discriminant of congruence number

Originally Posted by Zcyyu View Post
New function, new criterion, new theorem and new conjecture for discriminant of congruence
Zhou CongYao College of Information Science and Engineering, Hunan University
Yu Wei Department of statistics & financial engineering,College of mathematics and statistics,ningbo university
TangXiaoNing Beijing Haitian Start Technology Service Co., Ltd.
In this paper,a new function of congruence discrimination is proposed,namely,the upper bound estimation funtion of the number of solutions of the congruence.
If the value of this function is 1,the posttive integer A is noncongruent,this is the new N-1 criterion.Using this guideline, to history all 3 congruence negative theorms,a very simple elementary proof is given;and proved the author's newly discovered three modular 8-type congruence negative theorems;
At the same time,eight new congruences negation theorems(not model 8 types) are proved,by the way,we derive 1511 infinite sequences of noncongruent
If A is a congruence number,the value of this function is integer power of 2,that is,there are at least two types of solutions for congruence,one of them must be Fermat type,and each type has an infinite number of solutions.
Using this upper bound function, some new theorems for the number of congruence solutions are derived: the exact value of the solution is 2, 4, 8, 16, 32;
On this basis, a new conjecture is put forward: If the type of the congruence solution is used as an element, then these elements form a group,and the order of this group is integer power of 2 ,for any congruence, the conversion relationship between the types is fixed.

Keyword:congruence number,Elliptic Curves,Number Theory,Group

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I've tried it out and can download the full PDF correctly
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Old 2020-07-04, 11:21   #24
Jun 2020

1210 Posts
Default New function, new criterion, new theorem and new conjecture for discriminant of congruent number

Originally Posted by R.D. Silverman View Post
It is the responsibility of the author to make the paper readable. Your knowledge
of English is far superior to my knowledge of Mandarin. However, the paper is
poorly written. May I suggest that you re-write the paper with the help of someone
with a better knowledge of English? You should also read the Halmos' book: How
to Write Mathematics.
At the beginning, we used the translation software,
but the quality was a little bad.
I'm going to revise it carefully

thanks !
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