23 11 Article 19.8.1 Journal of Integer Sequences, Vol. 22 (2019), 2 3 6 1 47 Waring’s Problem for Hurwitz Quaternion Integers Janyarak Tongsomporn School of Science Walailak University Nakhon Si Thammarat 80160 Thailand tjanyarak@gmail.com Nicola Oswald Faculty for Mathematics and Natural Sciences Wuppertal University Gauß-Str. 20, Wuppertal 42119 Germany oswald@uni-wuppertal.de J¨ orn Steuding Department of Mathematics W¨ urzburg University Am Hubland, W¨ urzburg 97218 Germany steuding@mathematik.uni-wuerzburg.de 1