Totient numbers for cyclic group rings (Q1091419)

Let \(E_1\) be a rational subspace of \(\mathbb R^n\) which is orthogonal to the subspace \(E_0\) generated by the vector \((1,1,\ldots,1)\in \mathbb R^n\). The totient \(\varphi (E_1)\) of \(E_1\) is the smallest positive integer \(m\) which can be represented in the form \(m=v_1+\ldots+v_n\) where \(v=(v_1,\ldots,v_m)\in\mathbb Z^n\cap (E_0+E_1)\). The author determines the totient of the rational ring of cyclic groups.