  In this paper, we investigate the minimum number of triangles, denoted by
$t(n,k)$, in $n$-vertex $k$-regular graphs, where $n$ is an odd integer and $k$
is an even integer. The well-known Andr\'asfai-Erd\H{o}s-S\'os Theorem has
established that $t(n,k)>0$ if $k>\frac{2n}{5}$. In a striking work, Lo has
provided the exact value of $t(n,k)$ for sufficiently large $n$, given that
$\frac{2n}{5}+\frac{12\sqrt{n}}{5}<k<\frac{n}{2}$. Here, we bridge the gap
between the aforementioned results by determining the precise value of $t(n,k)$
in the entire range $\frac{2n}{5}<k<\frac{n}{2}$. This confirms a conjecture of
Cambie, de Joannis de Verclos, and Kang for sufficiently large $n$.
