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Number Theory with Computer Applications, 1st edition

Published by Pearson (August 4, 1997) © 1998

  • Ramanujachary Kumanduri
  • Christina Romero
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Appropriate for most courses in Number Theory.

This book effectively integrates computing algorithms into the number theory curriculum using a heuristic approach and strong emphasis on proofs. Its in-depth coverage of modern applications considers the latest trends and topics, such as elliptic curves—a subject that has seen a rise in popularity due to its use in the proof of Fermat's Last Theorem.



 1. Introduction.


 2. Divisibility and Primes.


 3. Modular Arithmetic.


 4. Fundamental Theorems of Modular Arithmetic.


 5. Cryptography.


 6. Primality Testing and Factoring.


 7. Primitive Roots.


 8. Applications.


 9. Quadratic Congruences.


10. Applications.


11. Continued Fractions.


12. Factoring Methods.


13. Diophantine Approximations.


14. Diophantine Equations.


15. Arithmetical Functions and Dirichlet Series.


16. Distribution of Primes.


17. Quadratic Reciprocity Law


18. Binary Quadratic Forms.


19. Elliptic Curves.


Appendix A: Mathematical Induction.


Appendix B: Binomial Theorem.


Appendix C: Algorithmic Complexity and O-notation.


Answers and Hints.


Index of Notation.


Index.

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