高等算术-第8版

IntroductionⅠ 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 primesⅡ Congruences1．The congruence notation2．Linear congruences3．Fermat's theorem4．Euler's function φ（m）5．Wilson's theorem6．Algebraic congruences7．Congruences to a prime modulus8．Congruences in several unknowns9．Congruences covering all numbersⅢ Quadratic Residues1．Primitive roots2．Indices3．Quadratic residues4．Gauss's lemma5．The law of reciprocity6．The distribution of the quadratic residuesⅣ 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 fractionsⅤ 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 squaresⅥ 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-numberⅦ 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 developmentsⅧ 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