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.