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Arithmetic of the IntegersIntroduction - Where We Begin and WhyThe Fundamental LawsDivisibilityPrime NumbersComputer Arithmetic and ComplexityApplications to a Set of QuadraticsCongruencesThe BasicsLinear CongruencesArithmetic Functions - Euler's TotientThe Chinese Remainder TheoremPolynomial Congruences and Thue's TheoremCryptography and FactoringQuadratic PolynomialsPrimitive RootsOrderExistenceIndicesPrimality Testing and CryptographyQuadratic Orders, Ideals and UnitsQuadratic ResiduesThe Quadratic Reciprocity LawThe Jacobi and Kronecker SymbolsQuadratic Polynomials and PrimesQuadratic Residues and Primality TestingApplications to Quadratic OrdersContinued FractionsFinite Continued FractionsInfinite Continued FractionsPeriodic Continued FractionsContinued Fractions and FactoringThe Continued Fraction AlgorithmDiophantine EquationsSums of SquaresThe Equation x2 - Dy2 = nDiophantine Equations of Higher DegreeElliptic Curves, Factoring, and PrimalityApplications: Algebraic Number TheoryAppendicesA. Set TheoryB. Primes = 9547 and Least Primitive RootsC. Tables of Special PrimesD. Cunningham FactorizationsE. Pseudoprimes and Carmichael NumbersF. IndicesG. Values of Some Arithmetic FunctionsH. The ABC ConjectureI. The Prime Number TheoremSolutions to Odd-Numbered ExercisesBibliographyList of SymbolsIndex