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20 - The Representation of a Number by Two or Four Squares

Table of contents

  • 20.1 Waring’s Problem: the Numbers g(k) and U(k)
  • 20.2 Squares
  • 20.3 Second Proof of Theorem 366
  • 20.4 Third and Fourth Proofs of Theorem 366
  • 20.5 The Four-Square Theorem
  • 20.6 Quaternions
  • 20.7 Preliminary Theorems about Integral Quaternions
  • 20.8 The Highest Common Right-Hand Divisor of Two Quaternions
  • 20.9 Prime Quaternions and the Proof of Theorem 370
  • 20.10 The Values of g(2) and G(2)
  • 20.11 Lemmas for the Third Proof of Theorem 369
  • 20.12 Third Proof of Theorem 369: the Number of Representations
  • 20.13 Representation by a Larger Number of Squares

20.1 Waring’s Problem: the Numbers g(k) and U(k)

20.2 Squares

20.3 Second Proof of Theorem 366

20.4 Third and Fourth Proofs of Theorem 366

20.5 The Four-Square Theorem

20.6 Quaternions

20.7 Preliminary Theorems about Integral Quaternions

20.8 The Highest Common Right-Hand Divisor of Two Quaternions

20.9 Prime Quaternions and the Proof of Theorem 370

20.10 The Values of g(2) and G(2)

20.11 Lemmas for the Third Proof of Theorem 369

20.12 Third Proof of Theorem 369: the Number of Representations

20.13 Representation by a Larger Number of Squares


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