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

Pentti Haukkanen, László Tóth

An integer $a$ is said to be regular (mod $r$) if there exists an integer $x$ such that $a^{2}x\equiv a(\mathrm{mod}r)$. In this paper we introduce an analogue of Ramanujan's sum with respe…