Homology of cyclic groups with trivial coefficients

Let $G$ be a cyclic group of order $n$ and let $A$ be a trivial $G$-module.

Cyclic-group homology conjecture.

$$\operatorname{H}_{n-1}^{\lambda}(G,A)\cong \begin{cases} A/2A, & n\equiv 0\pmod{2},\\ \operatorname{Ker}(\varphi_n:A\to A), & n\equiv 1\pmod{2}, \end{cases}$$

where $\varphi_n(a)=na$ for $a\in A$.

This gives an explicit description of the $(n-1)$-st exterior homology group for cyclic groups with trivial coefficients, separating the even- and odd-order cases. The supplied material does not indicate whether this assertion has been proved or remains open.