Introduction
Weil,whohasmadeoutstandingcontributionstonumbertheory,Wrotethe"NumberTheory:AHistoricalGuidefromHammurabitoLegendre",whichinterpretsthehistoryofnumbertheory;hisresearchcoversapproximatelythirty-sixcenturiesofarithmeticwork—fromapiecethatcanbetracedbacktoHanmuFromtheBabyloniantabletsoftheRabbinicaldynastytoLegendre's"OnNumbers"(1798).WeiYihasalwayshopedtotellreaderswithabettereducationalbackgroundabouthisresearchfield,whichpromptedhimtousehistoricalinterpretationmethodsintheanalysisofproblems,theevolutionofnumbertheorymethods,andtheirmeaninginmathematics.Inthecourseofhisdiscussion,Weilandreaderscametothestudiosofthefourmainauthorsofmodernnumbertheory(Fermat,Euler,Lagrange,Legendre),andconductedacarefulstudythere.,Inspectionwithacriticaleye."NumberTheory:AHistoricalGuidefromHammurabitoLegendre"isrichinthebroadcontentofknowledgehistory,andhasaveryimportantcontributiontounderstandingourculturalheritage.
Abouttheauthor
Author:(France)AndréWeilTranslator:XuMingweiSeriesEditor:QiuChengtongCommentary:WangYuan
A.Weil(AndreWeil,1906-1998),oneofthemostinfluentialmathematiciansofthe20thcentury,isoneofthefoundersandleadersofthefamousBourbakischoolinFrance.Hismaincontributionsareinthefieldsofalgebraicgeometry,numbertheory,grouptheory,andhistoryofmathematics.In1979,hewontheWolfPrizeforhis"excitingworkofintroducingalgebraicgeometryintonumbertheory".
ManyofWeiYi’sworksaremathematicsclassics,including"FoundationsofAlgebraicGeometry"(1946),"BasicNumberTheory"(BasicNumberTheory,1967),"TopologicalGroupsandTheirIntroductiontoApplications(LintegrationdanslesGroupesTopologiquesetsesAppfications,1940)andthisbook.
CatalogueofBooks
Prefaceto"MathematicsTranslationSeries"
Foreword
ListofIllustrations
Abbreviation,basicreferenceDocumentsandsigns
Chapter1NumberTheoryintheAboriginalPeriod
1.1Introduction
1.2PrimeNumbersandFactorization
1.3CompleteNumbers
1.4AProblem
1.5PythagoreanTriangle
1.6SumofTwoSquares
1.7FibonacciSum"TheSquareNumber"
1.8EarlyworkonPell'sequation
1.9Pell'sequation:ArchimedesandtheIndians
1.10LostEquationsofFantuandDiophantus
1.11DiophantusandtheSumofSquares
1.12TheRecoveryofDiophantus:VedicandBache
ChapterTwoFermatandhisletter
2.1Biography
2.2BinomialCoefficient
2.3Proofincomparisonwith"induction"
2.4PerfectnumbersandFermat'stheorem
2.5Initialexploration
2.6Thefirstattemptonthesecondremainder
2.7Theprimefactorofthesumoftwosquarenumbers
2.8Thesumoftwosquarenumbers
2.9Thenumberrepresentedbythesumoftwosquarenumbers
2.10Infinitedescentmethodandtheequationx4-y4=z2
p>2.11ProblemsinFermat'smatureperiod
2.12"Elementary"quadraticform
2.13Peerequation
2.14Quadraticindeterminateequation
2.15Tracingtheoriginoftheequationofgenus1
2.16Discussingthedescentmethodagain
2.17Conclusion
AppendixIEuclidGetthequadraticdomain
AppendixIIGenus1curveinprojectivespace
AppendixIIIFermat's"doubleequation"asaquarticcurveinspace
AppendixIVDescentMethodandModel'sTheorem
AppendixVEquationy2=x3-2x
ChapterThreeEuler
3.1SixteenthCentury,SeventeenthScientificactivitiesinthe20thand18thcenturies
3.2Euler’slife
3.3EulerandGoldbach
3.4Euler’sdiscoveryofnumbertheory
p>3.5RoleList(Dramatispersonae)
3.6MultiplicativeGroupsModuloIV
3.7"Real"vs."Virtual"
3.8MissTwoSub-ReciprocityLaw
3.9BinaryQuadraticForm
3.10Searchforlargeprimenumbers
p>3.11SumofFourSquareNumbers
3.12SquareRootandContinuedFraction
3.13QuadraticDiophantineEquation
3.14OnDiofanagainGraphequation
3.15ellipticintegralandadditivetheorem
3.16ellipticcurveasDiophantineequation
3.17summationformulaand∑n
3.18Euler'ssumfunction
3.19Trigonometricfunction
Functionalequationof3.20function
3.21Partitionumerorumandmodularfunction
p>3.22Conclusion
AppendixIQuadraticReciprocityLaw
AppendixIIAnelementaryproofofthesumofsquaresproblem
AppendixIIIEllipticcurveAdditionaltheorem
ChapterIVTransitionalPeriod:LagrangeandLegendre
4.1TheLifeofLagrange
4.2LagrangeandNumbertheory
4.3Indeterminateequations
4.4Lagrange’stheoryofbinaryquadraticforms
4.5Legendre’slife
4.6Legendre'sarithmeticwork
AppendixIHasseprincipleoftriplequadraticform
AppendixIILegendreproofofpositivebinaryquadraticform
AppendixIIIAProofofLagrange'sIndefiniteBinaryQuadraticForm
SupplementaryReferences
PostscriptofTranslation
WangYuanMr.LettertotheTranslator
NameIndex
ContentIndex