Introduction�� 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�� Congruences1��The congruence notation2��Linear congruences3��Fermat's theorem4��Euler's function �գ�m��5��Wilson's theorem6��Algebraic congruences7��Congruences to a prime modulus8��Congruences in several unknowns9��Congruences covering all numbers�� Quadratic Residues1��Primitive roots2��Indices3��Quadratic residues4��Gauss's lemma5��The law of reciprocity6��The distribution of the quadratic residues�� 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�� 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�� 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�� 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