About our author Kenneth H. Rosen received his BS in mathematics from the University of Michigan - Ann Arbor (1972) and his PhD in mathematics from MIT (1976). Before joining Bell Laboratories in 1982, he held positions at the University of Colorado - Boulder, The Ohio State University - Columbus, and the University of Maine - Orono, where he was an associate professor of mathematics. While working at AT&T Laboratories, he taught at Monmouth University, teaching courses in discrete mathematics, coding theory, and data security. Dr. Rosen has published numerous articles in professional journals in the areas of number theory and mathematical modeling. He is the author of Elementary Number Theory,  7th Edition and other books.

• The Integers Numbers and SequencesDiophantine ApproximationSums and ProductsMathematical InductionThe Fibonacci NumbersDivisibility Integer Representations and Operations Representations of IntegersComputer Operations with IntegersComplexity of Integer Operations Greatest Common Divisors Greatest Common Divisors and Their PropertiesThe Euclidean AlgorithmLinear Diophantine Equations Prime Numbers Prime NumbersThe Distribution of PrimesThe Fundamental Theorem of ArithmeticFactorization Methods and the Fermat Numbers Congruences Introduction to CongruencesLinear CongruencesThe Chinese Remainder TheoremPolynomial CongruencesSystems of Linear Congruences Applications of Congruences Divisibility TestsThe Perpetual CalendarRound-Robin TournamentsHashing FunctionsCheck Digits Some Special Congruences Wilson's Theorem and Fermat's Little TheoremPseudoprimesEuler's Theorem Arithmetic Functions The Euler Phi-FunctionThe Sum and Number of DivisorsPerfect Numbers and Mersenne PrimesMöbius InversionPartitions Cryptography Character CiphersBlock and Stream CiphersExponentiation CiphersPublic Key CryptographyCryptographic Protocols and Applications Primitive Roots The Order of an Integer and Primitive RootsPrimitive Roots for PrimesThe Existence of Primitive RootsDiscrete Logarithms and Index ArithmeticPrimality Tests Using Orders of Integers and Primitive RootsUniversal Exponents Applications of Primitive Roots and the Order of an Integer Pseudorandom NumbersThe EIGamal CryptosystemAn Application to the Splicing of Telephone Cables Quadratic Residues Quadratic Residues and NonresiduesThe Law of Quadratic ReciprocityThe Jacobi SymbolEuler PseudoprimesZero-Knowledge Proofs Decimal Fractions and Continued Fractions Decimal FractionsFinite Continued FractionsInfinite Continued FractionsPeriodic Continued FractionsFactoring Using Continued Fractions Nonlinear Diophantine Equations and Elliptic Curves Pythagorean TriplesFermat's Last TheoremSum of SquaresPell's EquationCongruent Numbers and Elliptic CurvesElliptic Curves Modulo PrimesApplications of Elliptic Curves The Gaussian Integers Gaussian Integers and Gaussian PrimesGreatest Common Divisors and Unique FactorizationGaussian Integers and Sums of Squares

About our author Kenneth H. Rosen received his BS in mathematics from the University of Michigan - Ann Arbor (1972) and his PhD in mathematics from MIT (1976). Before joining Bell Laboratories in 1982, he held positions at the University of Colorado - Boulder, The Ohio State University - Columbus, and the University of Maine - Orono, where he was an associate professor of mathematics. While working at AT&T Laboratories, he taught at Monmouth University, teaching courses in discrete mathematics, coding theory, and data security. Dr. Rosen has published numerous articles in professional journals in the areas of number theory and mathematical modeling. He is the author of Elementary Number Theory,  7th Edition and other books.

• The Integers Numbers and SequencesDiophantine ApproximationSums and ProductsMathematical InductionThe Fibonacci NumbersDivisibility Integer Representations and Operations Representations of IntegersComputer Operations with IntegersComplexity of Integer Operations Greatest Common Divisors Greatest Common Divisors and Their PropertiesThe Euclidean AlgorithmLinear Diophantine Equations Prime Numbers Prime NumbersThe Distribution of PrimesThe Fundamental Theorem of ArithmeticFactorization Methods and the Fermat Numbers Congruences Introduction to CongruencesLinear CongruencesThe Chinese Remainder TheoremPolynomial CongruencesSystems of Linear Congruences Applications of Congruences Divisibility TestsThe Perpetual CalendarRound-Robin TournamentsHashing FunctionsCheck Digits Some Special Congruences Wilson's Theorem and Fermat's Little TheoremPseudoprimesEuler's Theorem Arithmetic Functions The Euler Phi-FunctionThe Sum and Number of DivisorsPerfect Numbers and Mersenne PrimesMöbius InversionPartitions Cryptography Character CiphersBlock and Stream CiphersExponentiation CiphersPublic Key CryptographyCryptographic Protocols and Applications Primitive Roots The Order of an Integer and Primitive RootsPrimitive Roots for PrimesThe Existence of Primitive RootsDiscrete Logarithms and Index ArithmeticPrimality Tests Using Orders of Integers and Primitive RootsUniversal Exponents Applications of Primitive Roots and the Order of an Integer Pseudorandom NumbersThe EIGamal CryptosystemAn Application to the Splicing of Telephone Cables Quadratic Residues Quadratic Residues and NonresiduesThe Law of Quadratic ReciprocityThe Jacobi SymbolEuler PseudoprimesZero-Knowledge Proofs Decimal Fractions and Continued Fractions Decimal FractionsFinite Continued FractionsInfinite Continued FractionsPeriodic Continued FractionsFactoring Using Continued Fractions Nonlinear Diophantine Equations and Elliptic Curves Pythagorean TriplesFermat's Last TheoremSum of SquaresPell's EquationCongruent Numbers and Elliptic CurvesElliptic Curves Modulo PrimesApplications of Elliptic Curves The Gaussian Integers Gaussian Integers and Gaussian PrimesGreatest Common Divisors and Unique FactorizationGaussian Integers and Sums of Squares