  In this paper, we prove a local limit theorem for the distribution of the
number of triangles in the Erdos-Renyi random graph $G(n,p)$, where $p \in
(0,1)$ is a fixed constant. Our proof is based on bounding the characteristic
function $\psi(t)$ of the number of triangles, and uses several different
conditioning arguments for handling different ranges of $t$.
