Aequationes mathematicae

, Volume 75, Issue 1, pp 65–74

Hosszú’s equation over the Gaussian and Eisenstein integers


DOI: 10.1007/s00010-007-2883-9

Cite this article as:
Hajdu, G. & Hajdu, L. Aequ. math. (2008) 75: 65. doi:10.1007/s00010-007-2883-9


We consider Hosszú’s famous functional equation f(x) + f(y) = f(xy) + f(x + y − xy). We completely describe the set of functions \(f : R \rightarrow {\mathbb{A}}\) satisfying this equation, where R is the set of the Gaussian or Eisenstein integers and \({\mathbb{A}}\) is an arbitrary abelian group.

Mathematics Subject Classification (2000).



Hosszú’s functional equationfunctional equations

Copyright information

© Birkhäuser Verlag AG 2008

Authors and Affiliations

  1. 1.Institute of Mathematics and Computer Science, Faculty of Mechanical EngineeringSzent István UniversityGödöllőHungary
  2. 2.Institute of MathematicsUniversity of Debrecen and the Number Theory Research Group of the Hungarian Academy of SciencesDebrecenHungary