84208 20200513005823.0 doi 10.1016/j.jnt.2018.09.015 sideral 108572 ART-2018-108572 eng Grau, J.M. Fast computation of the number of solutions to x12+ ··· + xk2 = ¿ (mod n) 2018 Access copy available to the general public Unrestricted In 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]. info:eu-repo/semantics/openAccess by-nc-nd http://creativecommons.org/licenses/by-nc-nd/3.0/es/ 0.684 2018 MATHEMATICS 181 / 313 = 0.578 2018 Q3 T2 0.837 2018 Algebra and Number Theory 2018 Q1 info:eu-repo/semantics/article info:eu-repo/semantics/acceptedVersion (orcid)0000-0002-8191-3199 Oller-Marcén, A.M. 200 (2018), 427 - 440 J. number theory JOURNAL OF NUMBER THEORY 0022-314X 625881 http://zaguan.unizar.es/record/84208/files/texto_completo.pdf Postprint 47607 http://zaguan.unizar.es/record/84208/files/texto_completo.jpg?subformat=icon icon Postprint oai:zaguan.unizar.es:84208 articulos driver 2020-05-13-00:50:33 ARTICLE