doi:10.1007/s00605-015-0736-5engAyuso, PedroGrau, José MaríaOller Marcén, Antonio M.A von Staudt-type result for $\displaystyle{\sum_{z\in\mathbb{Z}_n[i]} z^k }$ART-2015-90661n this paper we study the sum of powers of the Gaussian integers Gk(n):=¿a,b¿[1,n](a+bi)k. We give an explicit formula for Gk(n)(modn) in terms of the prime numbers p=3(mod4) with p||n and p-1|k, similar to the well known one due to von Staudt for ¿ni=1ik(modn). We apply this result to study the set of integers n which divide Gn(n) and compute its asymptotic density with six exact digits: 0.971000….2015http://zaguan.unizar.es/record/3675010.1007/s00605-015-0736-5http://zaguan.unizar.es/record/36750oai:zaguan.unizar.es:36750MONATSHEFTE FUR MATHEMATIK 178, 3 (2015), 345-359by-nc-ndhttp://creativecommons.org/licenses/by-nc-nd/3.0/es/info:eu-repo/semantics/openAccess