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Conway, J.H. and Smith, D.A. (2003) On Quaternions and Octonions: Their Geometry, Arithmetic, and Symmetry. CRC Press, New York.
https://doi.org/10.1201/9781439864180

has been cited by the following article:

• TITLE: Three- and Four-Dimensional Generalized Pythagorean Numbers

  AUTHORS: Alfred Wünsche

  KEYWORDS: Number Theory, Pythagorean Triples, Tesseract, 4-Square Identity, Diophantine Equation

  JOURNAL NAME: Advances in Pure Mathematics, Vol.14 No.1, January 4, 2024

  ABSTRACT: The Pythagorean triples (a, b | c) of planar geometry which satisfy the equation a2+b2=c2 with integers (a, b, c) are generalized to 3D-Pythagorean quadruples (a, b, c | d) of spatial geometry which satisfy the equation a2+b2+c2=d2 with integers (a, b, c, d). Rules for a parametrization of the numbers (a, b, c, d) are derived and a list of all possible nonequivalent cases without common divisors up to d2 is established. The 3D-Pythagorean quadruples are then generalized to 4D-Pythagorean quintuples (a, b, c, d | e) which satisfy the equation a2+b2+c2+d2=e2 and a parametrization is derived. Relations to the 4-square identity are discussed which leads also to the N-dimensional case. The initial 3D- and 4D-Pythagorean numbers are explicitly calculated up to d2, respectively, e2.