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Elements of number theory

By: Material type: TextTextLanguage: English Series: Undergraduate texts in mathematicsPublication details: New York Springer 2003Description: xii, 254p. illISBN:
  • 0387955879 (HB)
Subject(s):
Contents:
1. Natural numbers and integers 2. The Euclidean algorithm 3. Congruence arithmetic 4. The RSA cryptosystem 5. The Pell equation 6. The Gaussian integers 7. Quadratic integers 8. The four square theorem 9. Quadratic reciprocity 10. Rings 11. Ideals 12. Prime ideals.
Summary: This book is a concise introduction to number theory and some related algebra, with an emphasis on solving equations in integers. Finding integer solutions led to two fundamental ideas of number theory in ancient times - the Euclidean algorithm and unique prime factorization - and in modern times to two fundamental ideas of algebra - rings and ideals." "The development of these ideas, and the transition from ancient to modern, is the main theme of the book. The historical development has been followed where it helps to motivate the introduction of new concepts, but modern proofs have been used where they are simpler, more natural, or more interesting.
Item type: BOOKS
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Holdings
Current library Home library Call number Materials specified Status Date due Barcode
IMSc Library IMSc Library 511 STI (Browse shelf(Opens below)) Available 50541

Includes index

Includes bibliography (p. 239-244) and references

1. Natural numbers and integers 2. The Euclidean algorithm 3. Congruence arithmetic 4. The RSA cryptosystem 5. The Pell equation 6. The Gaussian integers 7. Quadratic integers 8. The four square theorem 9. Quadratic reciprocity 10. Rings 11. Ideals 12. Prime ideals.

This book is a concise introduction to number theory and some related algebra, with an emphasis on solving equations in integers. Finding integer solutions led to two fundamental ideas of number theory in ancient times - the Euclidean algorithm and unique prime factorization - and in modern times to two fundamental ideas of algebra - rings and ideals." "The development of these ideas, and the transition from ancient to modern, is the main theme of the book. The historical development has been followed where it helps to motivate the introduction of new concepts, but modern proofs have been used where they are simpler, more natural, or more interesting.

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The Institute of Mathematical Sciences, Chennai, India