A full $m$-ary tree with $n$ vertices and  $i$ internal vertices has $n = m \cdot i + 1$ vertices and
$l = (m − 1)i + 1$ leaves.

How can I prove it?

I know that **$m$-ary tree** is a rooted tree such that every internal vertex has no more
than $m$ children. The tree is called a **full $m$-ary tree** if every internal vertex has exactly
$m$ children. An $m$-ary tree with $m = 2$ is called a binary tree.