Quaternion integers are quaternions whose components take on discrete values such as integers . . . . . . .
There are several kinds of quaternion integers:
Hurwitz quaternion (or Hurwitz integer) is a quaternion whose components are either all integers or all half-integers (a mixture of integers and half-integers is not allowed). The norm of a Hurwitz quaternion, given by a^2 + b^2 + c^2 + d^2, is always an integer.
A Lipschitz quaternion (or Lipschitz integer) is a quaternion whose components are all integers.
Wikipedia: Hurwitz quaternion
Fact archive: Quaternion
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