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1、FranzLemmermeyerNumbersandCurvesNovember11,2001Springer-VerlagBerlinHeidelbergNewYorkLondonParisTokyoHongKongBarcelonaBudapestFranzLemmermeyeremailfranzl@csusm.eduWWWhttp://www.rzuser.uni-heidelberg.de/～hb3/TableofContents1.TheNaturalNumbersN..........................
2、........11.1PeanoAxioms.........................................11.2Addition..............................................21.3Multiplication..........................................61.4Nasawell-orderedset..................................82.TheRingZofIntegers........
3、...........................132.1Addition..............................................142.2Multiplication..........................................162.3Zasanordereddomain.................................172.4Divisibility............................................193.
4、TheFieldQofRationalNumbers.........................213.1TheRationalNumbers..................................213.2Qasanordered?eld....................................244.TheArithmeticofZ......................................274.1Congruences.............................
5、..............274.2UniqueFactorizationinZ...............................294.3DiophantineEquations..................................374.4TheEuclideanAlgorithm................................415.ResidueClassRings......................................455.1Euler-Fermat...
6、.......................................465.2Euler’sPhiFunction....................................505.3PrimitiveRoots........................................516.Applications..............................................556.1RSA.........................................
7、.........556.2Flannery’sCayley-PurserAlgorithm......................576.3PrimalityTests.........................................596.4Pollard’sp?1-FactorizationMethod......................60viTableofContents7.QuadraticResidues.......................................637.
8、1QuadraticResidues.....................................637.2Gauss’sLemma........................................667.3TheQuad
