@BOOK{Apostol:76, AUTHOR = {T. A. Apostol}, TITLE = {Modular functions and {D}irichlet series in number theory}, PUBLISHER = {Springer-Verlag}, ADDRESS = {New York}, YEAR = {1976} } @BOOK{Apostol:84, AUTHOR = {T. Apostol}, TITLE = {Introduction to analytic number theory}, PUBLISHER = {Springer-Verlag}, ADDRESS = {New York}, YEAR = {1984} } @ARTICLE{Bach, AUTHOR = {E. Bach}, TITLE = {Towards a theory of {P}ollard's rho method}, JOURNAL = {Inf. Comput.}, VOLUME = {90}, YEAR = {1991}, PAGES = {139--155} } @INPROCEEDINGS{Cannon, AUTHOR = {J. Cannon}, TITLE = {A computational toolkit for finite permutation groups}, BOOKTITLE = {Proceeding of the Rutgers group theory year, 1983--1984}, EDITOR = {M. Aschbacher et. al.}, PUBLISHER = {Cambridge University Press}, ADDRESS = {Cambridge}, YEAR = {1984}, PAGES = {1--18} } @BOOK{Cohen, AUTHOR = {H. Cohen}, TITLE = {A course in computational algebraic number theory}, PUBLISHER = {Springer-Verlag}, ADDRESS = {New York}, YEAR = {1996} } @ARTICLE{CohenTeRiele, AUTHOR = {G. L. Cohen and H. J. J. {te Riele}}, TITLE = {Iterating the sum-of-divisors function}, JOURNAL = {Exp. Math.}, VOLUME = {5}, YEAR = {1996}, PAGES = {91--100} } @BOOK{Cohn:78, AUTHOR = {H. Cohn}, TITLE = {A classical invitation to algebraic numbers and class fields}, PUBLISHER = {Springer-Verlag}, ADDRESS = {New York}, YEAR = {1978} } @BOOK{Cohn:80, AUTHOR = {H. Cohn}, TITLE = {Advanced number theory}, PUBLISHER = {Dover}, ADDRESS = {New York}, YEAR = {1980} } @BOOK{Cohn:85, AUTHOR = {H. Cohn}, TITLE = {Introduction to the construction of class fields}, PUBLISHER = {Cambridge University Press}, ADDRESS = {Cambridge}, YEAR = {1985} } @BOOK{CohnPM, AUTHOR = {P. M. Cohn}, TITLE = {Algebra}, PUBLISHER = {John Wiley \& Sons}, ADDRESS = {London}, YEAR = {1974} } @BOOK{Cox, AUTHOR = {D. A. Cox}, TITLE = {Primes of the form $x^2+ny^2$}, PUBLISHER = {John Wiley and Sons}, ADDRESS = {New York}, YEAR = {1989} } @BOOK{Davenport, AUTHOR = {H. Davenport}, TITLE = {The higher arithmetic}, PUBLISHER = {Hutchinson \& Co. Ltd.}, ADDRESS = {London}, YEAR = {1952} } @BOOK{DavenportEtAl, AUTHOR = {H. Davenport and Y. Siret and E. Tournier}, TITLE = {Computer Algebra}, PUBLISHER = {Academic Press}, ADDRESS = {London}, YEAR = {1988} } @ARTICLE{Dixon, AUTHOR = {J. D. Dixon}, TITLE = {Computing subfields in algebraic number fields}, JOURNAL = {J. Austral. Math. Soc.}, VOLUME = {49}, YEAR = {1990}, PAGES = {434--448} } @BOOK{Gauss, AUTHOR = {C. F. Gauss}, TITLE = {Disquisitiones Arithmeticae}, PUBLISHER = {Springer-Verlag}, ADDRESS = {New York}, YEAR = {1986} } @ARTICLE{Gilbert, AUTHOR = {W. J. Gilbert}, TITLE = {Fractal geometry derived from complex bases}, JOURNAL = {Math. Intell.}, VOLUME = {4}, YEAR = {1982}, PAGES = {78--86} } @BOOK{Gouvea, AUTHOR = {F. Q. Gouv\^ea}, TITLE = {$p$-adic numbers: an introduction}, PUBLISHER = {Springer-Verlag}, ADDRESS = {Berlin}, YEAR = {1993} } @BOOK{HardyWright, AUTHOR = {G. H. Hardy and E. M. Wright}, TITLE = {An introduction to the theory of numbers}, PUBLISHER = {Oxford University Press}, ADDRESS = {Oxford}, YEAR = {1979} } @BOOK{HartleyHawkes, AUTHOR = {B. Hartley and T. O. Hawkes}, TITLE = {Rings, modules and linear algebra}, PUBLISHER = {Chapman and Hall}, ADDRESS = {London}, YEAR = {1970} } @BOOK{Hasse, AUTHOR = {H. Hasse}, TITLE = {Number Theory}, PUBLISHER = {Springer-Verlag}, ADDRESS = {Berlin}, YEAR = {1980} } @BOOK{Koblitz:87, AUTHOR = {N. Koblitz}, TITLE = {A course in number theory and cryptography}, PUBLISHER = {Springer-Verlag}, ADDRESS = {New York}, YEAR = {1987} } @BOOK{Knuth, AUTHOR = {D. E. Knuth}, TITLE = {The art of computer programming}, PUBLISHER = {Addison-Wesley}, ADDRESS = {Reading}, YEAR = {1981} } @ARTICLE{LewisMorton, AUTHOR = {D. J. Lewis and P. Morton}, TITLE = {Quotients of polynomials and a theorem of Pisot and Cantor}, JOURNAL = {Journal of the Faculty of Science, the University of Tokyo}, VOLUME = {28}, YEAR = {1982}, PAGES = {813--822} } @BOOK{LidlNiederreiter, AUTHOR = {R. Lidl and H. Niederreiter}, TITLE = {Finite fields}, SERIES = {Encyclopedia of Mathematics and Its Applications}, VOLUME = {20}, PUBLISHER = {Cambridge University Press}, ADDRESS = {Cambridge}, YEAR = {1996} } @BOOK{McCarthy, AUTHOR = {P. J. McCarthy}, TITLE = {Algebraic extensions of fields}, PUBLISHER = {Dover}, ADDRESS = {New York}, YEAR = {1966} } @BOOK{Marcus, AUTHOR = {D. A. Marcus}, TITLE = {Number fields}, PUBLISHER = {Springer-Verlag}, ADDRESS = {New York}, YEAR = {1977} } @ARTICLE{Martin-Lof, AUTHOR = {P. Martin-Lof}, TITLE = {The definition of random sequences}, JOURNAL = {Information and Control}, VOLUME = {9}, YEAR = {1966}, PAGES = {602--619} } @BOOK{Niven, AUTHOR = {I. Niven}, TITLE = {Irrational numbers}, PUBLISHER = {The Mathematical Association of America}, ADDRESS = {Washington DC}, YEAR = {1956} } @BOOK{PohstZassenhaus, AUTHOR = {M. Pohst and H. Zassenhaus}, TITLE = {Algorithmic algebraic number theory}, PUBLISHER = {Cambridge University Press}, ADDRESS = {Cambridge}, YEAR = {1989} } @ARTICLE{RamMurty, AUTHOR = {M. RamMurty}, TITLE = {Artin's conjecture for primitive roots}, JOURNAL = {Math. Intelligencer}, VOLUME = {10}, YEAR = {1988}, PAGES = {59--67} } @BOOK{Ribenboim, AUTHOR = {P. Ribenboim}, TITLE = {The book of prime number records}, PUBLISHER = {Springer-Verlag}, ADDRESS = {New York}, YEAR = {1988} } @BOOK{Samuel, AUTHOR = {P. Samuel}, TITLE = {Algebraic theory of numbers}, PUBLISHER = {Hermann}, ADDRESS = {Paris}, YEAR = {1970} } @BOOK{Serre, AUTHOR = {D. A. Serre}, TITLE = {A course in arithmetic}, PUBLISHER = {Springer-Verlag}, ADDRESS = {New York}, YEAR = {1973} } @BOOK{Stewart:89, AUTHOR = {I. Stewart}, TITLE = {Galois theory}, PUBLISHER = {Chapman and Hall}, ADDRESS = {London}, YEAR = {1989} } @ARTICLE{Shparlinskii, AUTHOR = {I. E. Shparlinskii}, TITLE = {On some problems in the theory of finite fields}, JOURNAL = {Russian Math. Surveys}, VOLUME = {46}, YEAR = {1991}, PAGES = {199--240} } @INCOLLECTION{Taussky, AUTHOR = {O. Taussky}, TITLE = {Introduction into connections between algebraic numbers and integral matrices}, BOOKTITLE = {A classical invitation to algebraic numbers and class fields}, EDITOR = {H. Cohn}, PUBLISHER = {Springer-Verlag}, ADDRESS = {New York}, YEAR = {1978}, PAGES = {305--326} } @BOOK{TenenbaumMendesFrance, AUTHOR = {G. Tenenbaum and M. Mend\`es France}, TITLE = {The prime numbers and their distribution}, PUBLISHER = {AMS}, ADDRESS = {Providence, Rhode Island}, YEAR = {2000} } @BOOK{ThomasWood, AUTHOR = {A. D. Thomas and G. V. Wood}, TITLE = {Group tables}, PUBLISHER = {Shiva}, ADDRESS = {Orpington, Kent}, YEAR = {1980} } @BOOK{Uspensky, AUTHOR = {J. V. Uspensky}, TITLE = {Theory of equations}, PUBLISHER = {McGraw-Hill Book Co.}, ADDRESS = {New York}, YEAR = {1948} } @ARTICLE{Vardi, AUTHOR = {I. Vardi}, TITLE = {Prime percolation}, JOURNAL = {Exp. Math.}, VOLUME = {7}, YEAR = {1998}, PAGES = {275--289} } @BOOK{Waerden, AUTHOR = {B. L. {van der Waerden}}, TITLE = {Algebra}, PUBLISHER = {Springer-Verlag}, ADDRESS = {New York}, YEAR = {1991} } @ARTICLE{Ward, AUTHOR = {M. Ward}, TITLE = {The arithmetical theory of linear recurring sequences}, JOURNAL = {Trans. Amer. Math. Soc.}, VOLUME = {35}, YEAR = {1933}, PAGES = {600--628} } @BOOK{Washington, AUTHOR = {L. C. Washington}, TITLE = {Introduction to cyclotomic fields}, PUBLISHER = {Springer-Verlag}, ADDRESS = {New York}, YEAR = {1982} }