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Abstract
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We use a representability theorem of G. L. Watson to examine sums of squares in
quaternion rings with integer coefficients. This allows us to determine a large family
of such rings where every element expressible as the sum of squares can be written as
the sum of three squares.
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Keywords
Waring's problem, quaternions, Hilbert–Waring theorem
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Mathematical Subject Classification
Primary: 11E25, 11P05
Secondary: 11R52
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Milestones
Received: 3 November 2020
Revised: 28 May 2021
Accepted: 27 June 2021
Published: 9 February 2022
Communicated by Kenneth S. Berenhaut
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