doi:10.1016/j.jnt.2018.09.015engGrau, J.M.Oller-Marcén, A.M.Fast computation of the number of solutions to x12+ ··· + xk2 = ¿ (mod n)ART-2018-108572In this paper we study the multiplicative function ¿k,¿(n) that counts the number of solutions of the equation x1 2+...+xk 2=¿(modn) in (Z/nZ)k. In particular we give closed explicit formulas for ¿k,¿(ps). This leads to an algorithm with an arithmetic complexity of constant order that improves previous work by Tóth [10] and completes the quadratic case considered by Li and Ouyang in [8].2018http://zaguan.unizar.es/record/8420810.1016/j.jnt.2018.09.015http://zaguan.unizar.es/record/84208oai:zaguan.unizar.es:84208JOURNAL OF NUMBER THEORY 200 (2018), 427 - 440by-nc-ndhttp://creativecommons.org/licenses/by-nc-nd/3.0/es/info:eu-repo/semantics/openAccess