English

An analogue of Ramanujan's sum with respect to regular integers (mod $r$)

Number Theory 2010-09-01 v1

Abstract

An integer aa is said to be regular (mod rr) if there exists an integer xx such that a2xa(modr)a^2x\equiv a\pmod{r}. In this paper we introduce an analogue of Ramanujan's sum with respect to regular integers (mod rr) and show that this analogue possesses properties similar to those of the usual Ramanujan's sum.

Keywords

Cite

@article{arxiv.1008.5239,
  title  = {An analogue of Ramanujan's sum with respect to regular integers (mod $r$)},
  author = {Pentti Haukkanen and László Tóth},
  journal= {arXiv preprint arXiv:1008.5239},
  year   = {2010}
}