The internal path length of a full binary tree is the sum, taken over all internal nodes of the tree, of the depth of each node. Likewise, the external path length is the sum, taken over all leaves of the tree, of the depth of each leaf. Consider a full binary tree with n internal nodes, internal path length i, and external path length e. Prove that e=i+2n
Ask yourself what does it mean for the tree to be "full". How many leaves does it have? Probably this should not be in the number theory forum.