A Pythagorean Introduction to Number Theory Right Triangles, Sums of Squares, and Arithmetic /

Right triangles are at the heart of this textbook's vibrant new approach to elementary number theory. Inspired by the familiar Pythagorean theorem, the author invites the reader to ask natural arithmetic questions about right triangles, then proceeds to develop the theory needed to respond. Thr...

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Bibliographische Detailangaben
1. Verfasser: Takloo-Bighash, Ramin (VerfasserIn)
Format: Elektronisch E-Book
Sprache:Englisch
Veröffentlicht: Cham : Springer International Publishing, 2018.
Ausgabe:1st ed. 2018.
Schriftenreihe:Undergraduate Texts in Mathematics,
Schlagworte:
Number theory.
ISBN:9783030026042
ISSN:0172-6056
Online-Zugang: Volltext
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Inhaltsangabe:
  • Part I Foundational Material
  • 1. Introduction
  • 2. Basic number theory
  • 3. Integral solutions to the Pythagorean Equation
  • 4. What integers are areas of right triangles?
  • 5. What numbers are the edges of a right triangle?
  • 6. Primes of the form 4k+1
  • 7. Gauss sums, Quadratic Reciprocity, and the Jacobi symbol
  • Part II Advanced Topics
  • 8. Counting Pythagorean triples modulo an integer
  • 9. How many lattice points are there on a circle or a sphere?
  • 10. What about geometry?
  • 11. Another proof of the four squares theorem
  • 12. Quadratic forms and sums of squares
  • 13. How many Pythagorean triples are there?
  • 14. How are rational points distributed, really?
  • Part III Appendices
  • A. Background
  • B. Algebraic integers
  • C. SageMath
  • References
  • Index.

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