Pythagoras number

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In mathematics, the Pythagoras number or reduced height of a field describes the structure of the set of squares in the field. The Pythagoras number p(K) of a field K is the smallest positive integer p such that every sum of squares in K is a sum of p squares.

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A Pythagorean field is a field with Pythagoras number 1: that is, every sum of squares is already a square.

Examples

Properties

Notes

  1. Lam (2005) p. 36
  2. Lam (2005) p. 398
  3. Rajwade (1993) p. 44
  4. Rajwade (1993) p. 228
  5. Rajwade (1993) p. 261
  6. Lam (2005) p. 396
  7. Lam (2005) p. 395

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