Disquisitiones arithmeticae
”
Dass die Aufgabe, die Primzahlen von den zusammengesetzten zu unterscheiden [. . . ] zu den
wichtigsten und n¨utzlichsten der gesamten Arithmetik geh¨ort [. . . ] ist so bekannt, dass es ¨uberfl¨ussig w¨are, hier ¨uber viele Worte zu verlieren. “
Carl Friedrich Gauß (1801)
Carl Friedrich Gauß (1777{1855):
"Zahlentheorie ist die Königin der Mathematik.
Mathematics is the queen of sciences and arithmetic the queen of mathematics
Carl Friedrich Gauss
The problem of distinguishing prime numbers from composite numbers and of resolving the latter into their prime factors is known to be one of the most important and useful in arithmetic. (. . . ) Further, the dignity of the science itself seems to require that every possible means be explored for the solution of a problem so elegant and so celebrated problem be zealously cultivated.
Carl Friedrich Gauss
« Le problème où l’on se propose de distinguer les nombres premiers des nombres composés, et
de résoudre ceux-ci en leurs facteurs premiers, est connu comme l’un des plus importants et des plus utiles de toute l’Arithmétique ; il a sollicité l’industrie et la sagacité des géomètres tant anciens que modernes, à un point tel qu’il serait superflu de discuter en détail à cet égard. [. . . ]
« De surcroît, la dignité de la science même semble demander que tous les secours possibles soient explorés avec soin pour parvenir à la solution d’un problème si élégant et si célèbre. »
« Problema, numeros primos a compositis dignoscendi, hosque in factores suos primos resoluendi,
ad grauissima ac utilissima totius Arithmeticæ pertinere, et geometrarum tum ueterum tum recentiorum
industriam ac sagacitatem occupauisse, tam notum est, ut de hac re copiose loqui superfluum
foret. [. . . ]
« Prætereaque scientiæ dignitas requirere uidetur, ut omnia subsidia ad solutionem problematis
tam elegantis ac celebris sedulo excolantur. »
Disquisitiones Arithmeticæ
de Gauß est, dans le texte latin :
Johann Carl Friedrich Gauß, Disquisitiones Arithmeticæ, 329.
2.Keyword
素性测试算法
素性测定 page
primality prime
Prime number
testing test prove proving
Primzahltests
test de primalité
nombres premiers
Πρώτοι αριθμοί
δοκιμές αριθμό
проверки простоты чисел
Randomized (Probalistic) Provable Primality Testing
Deterministic Primality Testing
AKS Primality testing
AKS Primality test
AKS Prime testing
AKS Prime test
AKS Primzahltests
AKS test de primalité nombres premiers
Le test de primalité AKS
AKS δοκιμές αριθμό
AKS проверки простоты чисел
Prime number
3.Introduction
3.1.The Aim of Thesis
3.2.The Scope of Thesis
3.3.Research Hierarchical Diagram
5.Presentation Styles
用各种IT技术
Interactive
Short texts
Electronically available only
Electronic formats
Strictly local yet
Easy to read even for laymen and like lovestory
Use as much as drawings, pictures.animations as possible to accompany or replace texts
Pictures
Drawings 图 三维图标
表
Graphs
Charts
Pies
SLIDES
PPT
Flash SWF Slides
OTHER FORMS OF SLIDES
EBOOKS IN CHM, HLP, EXE OR OTHERS
Movies and Animations
3D
VRML
FLASH MOVIES
web audio and video
streaming
QUICKTIME
REALMEDIA
WINDOWSMEDIA
WEB PORTAL
web incl web2.0
html
php
java
SOFTWARE
DATABASE
MOBILE AND HANDHELD DEVICES
DVD/VCDS
USB
网络多媒体
multimedia)
6.Structure of Writing
Newton or Euclid styles
Give every definiyion, axiom, proposition, theorem, corrolary etc a serial number and a name
conventions or notations
Common Notions
Πρώτοι Αριθμοί
Definitions
Terms
Terminology
Etymology
Encyclopedia
Glossary
Lexicon
Nomenclature
Abbreviations
List of Symbols
Index
Axiom
Principles
Assertion
Assumptions
Hypothesis
Conjecture
Suggestion
Common Notions
Fact
Proposition
If we can prove a statement true, then that statement is called a proposition.
a proposition is a less important or less fundamental assertion,
Predicates
Theory
Laws
Lemma
If a theorem is not particularly interesting, but is useful in proving an interesting statement,
then it’s often called a lemma. This one is found in Euclid’s Elements.
Sometimes instead of proving a theorem or proposition all at once, we break the proof down into modules; that is, we prove several supporting propositions, which are called lemmas, and use the results of these propositions to prove the main result.
a lemma is something that we will use later in this book to prove a proposition or theorem,
Statement
Rules
Porism
Theorem
A proposition of major importance is called a theorem.
a theorem is a deeper culmination of ideas,
A theorem is a valid implication of sufficient interest to warrant special attention.
If we can prove a proposition or a theorem, we will often, with very little effort, be able to derive other related propositions called corollaries.
a corollary is an easy consequence of a proposition, theorem, or lemma.
Collonary
A corollary is a theorem that logically follows very simply from a theorem. A corollary is a theorem that logically follows very simply from a theorem. Sometimes it follows from part of the proof of a theorem rather than from the statement of the theorem. In any case, it should be easy to
see why it’s true.
Collonary
A corollary is a theorem that logically follows very simply from a theorem. A corollary is a theorem that logically follows very simply from a theorem. Sometimes it follows from part of the proof of a theorem rather than from the statement of the theorem. In any case, it should be easy to
see why it’s true.
Postulations
Scholium
Conclusions
Consequence
Comment
Remark
Observation
Claim
Proof
Equations
Formulas
Note
Caveat
Thesis
Conics
Literature Reference / Bibliography
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Books
-
Databases
-
Multimedia
-
Websites
-
-
Theses
-
Proceedings
-
Papers
-
Presentations/Slides
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