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

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

2010-08-31

arxiv.org/abs/1008.5239v1

Mathematics

Number Theory

Scientific paper

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

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