1.23 In triangle $ABC$, $AB=33$, $AC=21$, and $BC=m$, where $m$ is a positive integer. If there exists a point $D$ on $AB$ and a point $E$ on $AC$ such that $AD=DE=EC=n$, where $n$ is a positive integer, what value must $m$ take?
(Swedish Mathematical Competition, 1982)