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Introduction¢ñ Factorization and the Primes1£®The laws of arithmetic2£®Proof by induction3£®Prime numbers4£®The fundamental theorem of arithmetic5£®Consequences of the fundamental theorem6£®Euclid's algorithm7£®Another proof of the fundamental theorem8£®A property of the H£®C£®F9£®Factorizing a number10£®The series of primes¢ò Congruences1£®The congruence notation2£®Linear congruences3£®Fermat's theorem4£®Euler's function ¦Õ£¨m£©5£®Wilson's theorem6£®Algebraic congruences7£®Congruences to a prime modulus8£®Congruences in several unknowns9£®Congruences covering all numbers¢ó Quadratic Residues1£®Primitive roots2£®Indices3£®Quadratic residues4£®Gauss's lemma5£®The law of reciprocity6£®The distribution of the quadratic residues¢ô Continued Fractions1£®Introduction2£®The general continued fraction3£®Euler's rule4£®The convergents to a continued traction5£®The equation ax-by=16£®Infinite continued fractions7£®Diophantine approximation8£®Quadratic irrationals9£®Purely periodic continued fractions10£®Lagrange's theorem11£®Pell's equation12£®A geometricalinterpretation of continued fractions¢õ Sums of Squares1£®Numbers representable by two squares2£®Primes of the form 4k+13£®Constructions for x and y4£®Representation by four squares5£®Representation by three squares¢ö Quadratic Forms1£®Introduction2£®Equivalent forms3£®The discriminant4£®The representation of a number by a form5£®Three examples6£®The reduction of positive definite forms7£®The reduced forms8£®The number of representations9£®The class-number¢÷ Some Diophantine Equations1£®Introduction2£®The equation x2+y2=z23£®The equation ax2+by2=z24£®Elliptic equations and curves5£®Elliptic equations modulo primes6£®Fermat's Last Theorem7£®The equation x3+y3=z3+w38£®Further developments¢ø Computers and Number Theory1£®Introduction2£®Testing for primality3£®'Random' number generators4£®Pollard's factoring methods5£®Factoring and primality via elliptic curves6£®Factoring large numbers7£®The Diffie-Hellman cryptographic method8£®The RSA cryptographic method9£®Primality testing revisitedExercisesHintsAnswersBibliographyIndex