Journal of Integer Sequences, Vol. 23 (2020), Article 20.4.4

Sums of Cubes in Quaternion Rings

Madison Gamble, Spencer Hamblen, Blake Schildhauer, and Chung Truong
Department of Mathematics and Computer Science
McDaniel College
Westminster, MD 21157


We investigate a version of Waring's problem over quaternion rings, focusing on cubes in quaternion rings with integer coefficients. We determine the global upper and lower bounds for the number of cubes necessary to represent all such quaternions.

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Received October 6 2019; revised versions received February 22 2020; February 23 2020. Published in Journal of Integer Sequences, March 20 2020.

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